diff --git a/pkg/ccl/logictestccl/testdata/logic_test/multi_region_query_behavior b/pkg/ccl/logictestccl/testdata/logic_test/multi_region_query_behavior
index 6307471dbd81..d1117c83930a 100644
--- a/pkg/ccl/logictestccl/testdata/logic_test/multi_region_query_behavior
+++ b/pkg/ccl/logictestccl/testdata/logic_test/multi_region_query_behavior
@@ -410,7 +410,7 @@ vectorized: true
                   table: orders@orders_pkey
                   spans: [/'ap-southeast-2'/'94e4b847-8f2f-4ac5-83f1-641d6e3df727' - /'ap-southeast-2'/'94e4b847-8f2f-4ac5-83f1-641d6e3df727'] [/'us-east-1'/'94e4b847-8f2f-4ac5-83f1-641d6e3df727' - /'us-east-1'/'94e4b847-8f2f-4ac5-83f1-641d6e3df727']
 ·
-Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJyslM1uGjEQx-99CmsuaSMT9otAVorkKKUtEYUUIrVSjdBmPSRuwN7a3nariFOfre9V7S4hISpUSXsA2-P5M_Mbz3AL9uscYuh-Ou-f9Abk5eve-GL8of-KjLv97ukF0UagmUpBSWb0QtuDalkZZIrkZFxvpt-lu9a5m1YOd7f7REib6ly5Tcfai7wZDd_XISw5G_YGqyBkeLc7kGqmCeO554W48qxtH991R911euSY7B1FGF12onajMwtmjShJW41OOPMbh5EvDjEUs3bQ3gMKSgscJAu0EH-GCCYUMqNTtFab0nRbOfREAbFHQaosd6V5QiHVBiG-BSfdHCGGi-RyjiNMBJqmBxQEukTOq5-tM2X1Ms1u8AdQONXzfKFsvFFUmSIlJRFQGGdJed3kwDg0OXBeHEWcF1h-XXbecl50Zs2zXz85L2a-4LzwhTouD-09Dk2PJEoQn2h3jQYmSwo6d_fpW5dcIcT-kj4P0f-_iCWM9yzMrWjBVrR7IotGJnOSqypDFBtQk-UfajDQDZ01g036vlxIR_ytqXhPqXJPfUPjUJxpqdA0w81Q9SSwepmWdZxKUQBdy7pFZghrrceEhQ9f4n5gV08wzF1MmE9ZQFlIWbSVIXwKQ5n7qlGiXfmvGqWv9U2ekS9aKqJVTFgpGg4Ia_8V4-4fZQ00QiXQVEyEtShhQfnZZ4dbyaKnkI3QZlpZfNQp2959QgHFFdZdZ3VuUjw3Oq3C1MdhpasMAq2rb4P60FPVVTWkD8X-v4iDneJwQ-w9Foc7xdFucbRT3Hoknixf_A4AAP__TIEqRA==
+Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJyslN1u2koQx-_PU6zmJudES_AnEEuRNsqhLRGFFCK1Uhchxzsk28Cuu163riKu-mx9r8o2-SCqqUh7Aeudmb9nfrOzvoPs8xIi6H-4GJ4ORuTf_wfTy-m74X9k2h_2zy6JNgLNXApKUqNXOjuqlo1BJkhOp_XD_Ku0Nzq38yrg3ntIhMwSnSu7HVhHkVeT8ds6RUbOx4PRJgkZ3z8dSbXQhPHccXzcRNa292_6k_5DeeSEHBwHGFz1gm6rt_AWrSBOwlbPX7itTuCKDvpi0fW6B0BBaYGjeIUZRB8hgBmF1OgEs0yb0nRXBQxEAZFDQao0t6V5RiHRBiG6AyvtEiGCy_hqiROMBZq2AxQE2lguq9fWlbJ6mae3-A0onOllvlJZtNVUmSAlJRFQmKZx6W5zYBzaHDgvjgPOCyz_rnqvOS96i_b5j--cFwtXcF64Qp2Um-4Bh7ZDYiWIS7S9QQOzNQWd28fyMxtfI0Tumr4M0f27iCWM8yLMRjSvEe2RKEMj4yXJVVUhii2o2foXPRjplk7b3jb9UK6kJW5jKc4-XR6oL2gsinMtFZq2v52qvgmsXuZlH-dSFEAfZP0iNYSFD9eE-U9P4vHCbo5gnNuIMJcyjzKfsqCRwd-Hoax9MyjBrvo3gzLU-jZPySctFdEqIqwUjUeEdX-Lcf9FaQIKKetQ1m3ECvbBqg8_3CaaoBJoqpyEBZQwr_wdsrAxZ7hPzglmqVYZPhvNpkGbUUBxjfWYZzo3CV4YnVRp6u240lUGgZmtvV69GajKVX0VnordPxF7O8X-lth5LvZ3ioPd4mCnONwtDneKO8_Es_U_PwMAAP__O2xhIQ==
 
 # Regression test for #74890. Code should not panic due to distribution already
 # provided by input.
diff --git a/pkg/sql/logictest/testdata/logic_test/pg_catalog b/pkg/sql/logictest/testdata/logic_test/pg_catalog
index 938d6c8c7418..b0eaf5da2968 100644
--- a/pkg/sql/logictest/testdata/logic_test/pg_catalog
+++ b/pkg/sql/logictest/testdata/logic_test/pg_catalog
@@ -4610,3 +4610,8 @@ WHERE
     AND t.typname LIKE 'myt%';
 ----
 0
+
+# Regression test for a panic after physical planning combined rendering steps
+# (#95633).
+statement ok
+SELECT d.datname, pg_catalog.pg_get_userbyid(d.datdba) FROM pg_catalog.pg_database d;
diff --git a/pkg/sql/opt/exec/execbuilder/testdata/distsql_merge_join b/pkg/sql/opt/exec/execbuilder/testdata/distsql_merge_join
index 89c41eeadfff..10194bf0102d 100644
--- a/pkg/sql/opt/exec/execbuilder/testdata/distsql_merge_join
+++ b/pkg/sql/opt/exec/execbuilder/testdata/distsql_merge_join
@@ -823,7 +823,7 @@ vectorized: true
           table: outer_c1@outer_c1_pkey
           spans: FULL SCAN
 ·
-Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJzMll9r4kAUxd_3Uwz3SbcjyeSPtYGFFNcuFqtdtbCwSEmTuyprM9lJhC3F774kqbiGNpMwKr5IMpnf3DnnXDN5hfjPChzo_bgfXPeHpPG1P5lOvg-aZNIb9LpT8pncjEd3hK8TFI8RIzcPgwG5HfWHb0M-Iw-T_vAbaUTLgDWBQsgDHHrPGIPzExhQMICCCRQsoGDDjEIkuI9xzEU65TUD-sFfcHQKyzBaJ-nwjILPBYLzCskyWSE4MPWeVjhGL0ChpesGmHjLVVZmuz13e_EY_cYXoNDlq_VzGDsk3R0lkZeCk8hLhzS9pdnECwPCCE8WKGC2oelSb1vYVX56IQsvXuzXdBnMNjMKceLNERy2oR9I2a3DRYACg-I6F2nh3ax1-N68rFbRkjsUc7zlyxCFdrm_7PQlQiePa_Qw7Y2z0IDCCn8lDZddNL-I5XyRXwKFMYYBCod0R9eD3qTba7iMumaTEtegxLUocW1K3HbBop18s4L8GsKGvMUjjbHCzPdrW3u1WfUuMg7RRXZLY_qR2oidvo06Z9RGRvUozUNEyfSWxo71SjBOn-XVGWVpVs_SOkiWdkszjvW_NE-fJdPPKEyrepj6AcJsaccKsoYQ-z0h_laI_5EQf_trUOLviVKSYXwo40T92D6jdpR8OI4xjngYY6WPCT0VjsEccy9jvhY-3gvuZ2Xy21HGZcdzgHGSP2Vvd_0wf5busAatAlsqcFsF7pTDrAjr_8NGOWyUwmyf1ou0qRSWhFaBJWGVw5KwymFJWJZKWLaS3RJaBZbYXQ5L7C6HJXa3Vey-VLJbQqvAErvLYYnd5bDE7o6K3VdKdktoFVhidzkssbsclr35ax2WRl1cibaU6LYS3ZHQ9U7M2ebTvwAAAP__BTlqQg==
+Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJzEVu9r4koU_f7-iuF-0teRZPLD2sCDFJ99WKz2qYWFRUqa3FVZm8lOImwp_u9LTMTV1YxhjH4Rk8yZc-49J3fyCfGPBTjQ-fLcu-_2Se3f7mg8-r9XJ6NOr9Mek7_Jw3DwRPgyQfEaMfLw0uuRx0G3n9_yGXkZdfv_kVo0D1gdKIQ8wL73jjE4X4EBBQMomEDBAgo2TChEgvsYx1ykSz7XgG7wExydwjyMlkl6e0LB5wLB-YRkniwQHBh7bwscoheg0NJ9A0y8-WJNs5Hnbv68Rt_xAyi0-WL5HsYOSdVREnkpcBR56S1Nb2g28cKAMMKTGQqYrGi6VS5hy_z2QWZePNvldBlMVhMKceJNERy2okdK2e7DRYACg_19blLi7apleGjdmmu_JU8opvjI5yEK7XZ32_FHhE5m1-Bl3BmuTQMKC_yW1Fx2U_9HzKez7C9QGCwTh7iMugZ1Tepa1LWp29zryLZa82i1B1T2eYNHGjN2BQ4xDFA4pD2473VG7U4tZTfrlLgGJa5FiWtTUiDBOqHhJVqZi2zurTzMbe9ws9Nza5wjt3ZDY3pFwWWXD27resGVOJdnwqwyuMbp4THPER6mNzRW1dgzLp-eu-ulR2Jdnh6ryvSYp6fHOkt67IZmVDV7zMunh-nXi4_Euzw-dpXxsU6Pj36G-DS0qqJTohD7UCH-phD_WCH-5tegxN8pSqkM42gZF3oDmtd7ASSm5S8Au9Rn4wEJQ4wjHsZ40kehnrYagylm7sV8KXx8Ftxf02SXgzVu_eERYJxkT5mdXXXD7FmqsARaBazE3FKSLdHN9tH672hjB6zvg41CsFnMbBaC2W0xtaVktQStAlZillgtkS3RbRc2vFnc76aK1bdKZknQKmAlZolZEtkS3a3Cft8Vm3WnYhZTm6IyuBJajVtimEy5THrxKGWSWcqUhin7Y5qWM00CV0KrcctMkyiXSS91jhhl4UpoNe6WmnKZ9OLDhElOE1buOJms_voVAAD__whhgYA=
 
 query T
 EXPLAIN (VERBOSE) SELECT * FROM outer_gc1 FULL OUTER JOIN outer_c1 USING (pid1, cid1, cid2)
@@ -883,7 +883,7 @@ vectorized: true
           table: outer_c1@outer_c1_pkey
           spans: FULL SCAN
 ·
-Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJyckt9um0wQxe-_p1jNlf15InvB6R-kShu5pCIidgpYqlRZEWWnFJWwdBekRpbfvQJax6DYcXuD2LNzht8ZZgvmRw4OuJ_u_CtvyUbvvTAKP_pjFrq-u4jY_-w6WN0yVVek79OEs-u177Oblbf8rSWcrUNv-YGNykxyZMmfpzUGhEJJWsYPZMD5DBwQLmGDUGqVkDFKN_K2LfLkT3BmCFlR1lUjbxASpQmcLVRZlRM4sFQXqpzagCCpirO8LdshqLp6MpkqTgmc-Q4PGvPTjaP4S04BxZL0dNZrD_vgYv92X36nR0BYqLx-KIzDhsGRpd0hTeImc1jGTdkFHIPl_wrLn4Pds56FeiaidRTxiawulJakSQ7_0Mslz-S8JZ3SjcoK0lOrnzN6LMnpNnG1jtyg3UdAyOlrNRJ8gsKaoLAn43c6S7_1JUAIqJCkHbZYXfluuHBHgqN4NcYDwULxuifYKN6MkYk5MnGJTLw9Oim7N6kXVjogU6rC0Fk7PWvGRDKlbuxG1TqhO62S9jPdcdX6WkGSqbrbeXfwiu6qATw085Nmu2fmQ7P1F2ZraLZPmmcD7M3uv18BAAD__7KcfNU=
+Diagram: https://cockroachdb.github.io/distsqlplan/decode.html#eJyck1Fvm0AMx9_3KU5-ShZXyQFpO6RJV2V0oqKhC4k0aYoqBh5Doxw7DmlVlO8-AVsaooamfUH4f_6bn7FvA-XvDGxwvt55V-6cDT65wTL44g1Z4HjObMnes-uFf8tkpUndJxFn1yvPYze-O_-nRZytAnf-mQ2KNObIov9PYwgIuYxpHj5QCfY34IAwhTVCoWREZSlVLW-aJDf-A_YEIc2LStfyGiGSisDegE51RmDDXJ7JYmwBQkw6TLMmbYsgK_1kKnWYENjTLe4V5v2Fl-H3jBYUxqTGk0552DUudm_3xS96BISZzKqHvLTZYePIkjZIorDuOSjCOu0MjsHyt8Ly52B3rCehnohoHEV8IqtyqWJSFB9O6OWUZ_q8JZXQjUxzUmOj2-fysSC73UR_tXQWzT4CQkY_9EDwEQpjhMIcDT-qNPnZlQDBr7TNBEdhoDBRWCimKM5RXKC4RPHh6D8wXzOmdlnNLviC8piUzWb-lecEM2dQU5wPcU8wUFx0BBPF5RCZsJCJKbIePqvD98JlWlBZyLykk27TpB4QxQm1Ay9lpSK6UzJqPtOGfuNrhJhK3Z5O28DN26MacN_Me81mx8wPzcYrzMah2ew1W_3YVq95cmBeb9_9DQAA__8XQ7Wb
 
 query T
 EXPLAIN (VERBOSE) SELECT * FROM outer_c1 LEFT OUTER JOIN outer_p1 USING (pid1) WHERE pid1 >= 0 AND pid1 < 40
diff --git a/pkg/sql/physicalplan/physical_plan.go b/pkg/sql/physicalplan/physical_plan.go
index f3733a56c7ae..b97453ab5221 100644
--- a/pkg/sql/physicalplan/physical_plan.go
+++ b/pkg/sql/physicalplan/physical_plan.go
@@ -662,11 +662,11 @@ func (p *PhysicalPlan) AddRendering(
 	}
 
 	post := p.GetLastStagePost()
-	if len(post.RenderExprs) > 0 {
+	if len(post.RenderExprs) > 0 || len(post.OutputColumns) > 0 {
 		post = execinfrapb.PostProcessSpec{}
-		// The last stage contains render expressions. The new renders refer to
-		// the output of these, so we need to add another "no-op" stage to which
-		// to attach the new rendering.
+		// The last stage contains render expressions, or is projecting input columns.
+		// The new renders refer to the output of these in a particular order, so we
+		// need to add another "no-op" stage to which to attach the new rendering.
 		p.AddNoGroupingStage(
 			execinfrapb.ProcessorCoreUnion{Noop: &execinfrapb.NoopCoreSpec{}},
 			post,
diff --git a/pkg/sql/physicalplan/physical_plan_test.go b/pkg/sql/physicalplan/physical_plan_test.go
index 67e075944726..4275da7c22c3 100644
--- a/pkg/sql/physicalplan/physical_plan_test.go
+++ b/pkg/sql/physicalplan/physical_plan_test.go
@@ -163,7 +163,6 @@ func TestProjectionAndRendering(t *testing.T) {
 				); err != nil {
 					t.Fatal(err)
 				}
-
 			},
 
 			expPost: execinfrapb.PostProcessSpec{
@@ -172,6 +171,38 @@ func TestProjectionAndRendering(t *testing.T) {
 			},
 			expResultTypes: "B,D,C",
 		},
+
+		// Rendering after projection.
+		{
+			post: execinfrapb.PostProcessSpec{
+				Projection:    true,
+				OutputColumns: []uint32{3, 1, 4, 2},
+			},
+			resultTypes: "A,B,C,D",
+
+			action: func(p *PhysicalPlan) {
+				if err := p.AddRendering(
+					context.Background(),
+					[]tree.TypedExpr{
+						&tree.IndexedVar{Idx: 0},
+						&tree.IndexedVar{Idx: 1},
+						&tree.IndexedVar{Idx: 2},
+					},
+					fakeExprContext{},
+					[]int{2, 0, 3, 1},
+					[]*types.T{strToType("C"), strToType("A"), strToType("D")},
+					execinfrapb.Ordering{},
+				); err != nil {
+					t.Fatal(err)
+				}
+			},
+
+			expPost: execinfrapb.PostProcessSpec{
+				Projection:    true,
+				OutputColumns: []uint32{4, 3, 2},
+			},
+			expResultTypes: "C,A,D",
+		},
 	}
 
 	for testIdx, tc := range testCases {