diff --git a/x-pack/plugins/task_manager/server/task_store.test.ts b/x-pack/plugins/task_manager/server/task_store.test.ts
index d65c39f4f454..a02123c4a3f8 100644
--- a/x-pack/plugins/task_manager/server/task_store.test.ts
+++ b/x-pack/plugins/task_manager/server/task_store.test.ts
@@ -627,7 +627,7 @@ if (doc['task.runAt'].size()!=0) {
       });
     });
 
-    test('it returns task objects', async () => {
+    test('it filters out running tasks', async () => {
       const taskManagerId = uuid.v1();
       const claimOwnershipUntil = new Date(Date.now());
       const runAt = new Date();
@@ -641,7 +641,7 @@ if (doc['task.runAt'].size()!=0) {
               taskType: 'foo',
               schedule: undefined,
               attempts: 0,
-              status: 'idle',
+              status: 'claiming',
               params: '{ "hello": "world" }',
               state: '{ "baby": "Henhen" }',
               user: 'jimbo',
@@ -715,7 +715,103 @@ if (doc['task.runAt'].size()!=0) {
           runAt,
           scope: ['reporting'],
           state: { baby: 'Henhen' },
-          status: 'idle',
+          status: 'claiming',
+          taskType: 'foo',
+          user: 'jimbo',
+          ownerId: taskManagerId,
+        },
+      ]);
+    });
+
+    test('it returns task objects', async () => {
+      const taskManagerId = uuid.v1();
+      const claimOwnershipUntil = new Date(Date.now());
+      const runAt = new Date();
+      const tasks = [
+        {
+          _id: 'aaa',
+          _source: {
+            type: 'task',
+            task: {
+              runAt,
+              taskType: 'foo',
+              schedule: undefined,
+              attempts: 0,
+              status: 'claiming',
+              params: '{ "hello": "world" }',
+              state: '{ "baby": "Henhen" }',
+              user: 'jimbo',
+              scope: ['reporting'],
+              ownerId: taskManagerId,
+            },
+          },
+          _seq_no: 1,
+          _primary_term: 2,
+          sort: ['a', 1],
+        },
+        {
+          _id: 'bbb',
+          _source: {
+            type: 'task',
+            task: {
+              runAt,
+              taskType: 'bar',
+              schedule: { interval: '5m' },
+              attempts: 2,
+              status: 'claiming',
+              params: '{ "shazm": 1 }',
+              state: '{ "henry": "The 8th" }',
+              user: 'dabo',
+              scope: ['reporting', 'ceo'],
+              ownerId: taskManagerId,
+            },
+          },
+          _seq_no: 3,
+          _primary_term: 4,
+          sort: ['b', 2],
+        },
+      ];
+      const {
+        result: { docs },
+        args: {
+          search: {
+            body: { query },
+          },
+        },
+      } = await testClaimAvailableTasks({
+        opts: {
+          taskManagerId,
+        },
+        claimingOpts: {
+          claimOwnershipUntil,
+          size: 10,
+        },
+        hits: tasks,
+      });
+
+      expect(query.bool.must).toContainEqual({
+        bool: {
+          must: [
+            {
+              term: {
+                'task.ownerId': taskManagerId,
+              },
+            },
+            { term: { 'task.status': 'claiming' } },
+          ],
+        },
+      });
+
+      expect(docs).toMatchObject([
+        {
+          attempts: 0,
+          id: 'aaa',
+          schedule: undefined,
+          params: { hello: 'world' },
+          runAt,
+          scope: ['reporting'],
+          state: { baby: 'Henhen' },
+          status: 'claiming',
           taskType: 'foo',
           user: 'jimbo',
           ownerId: taskManagerId,
@@ -728,7 +824,7 @@ if (doc['task.runAt'].size()!=0) {
           runAt,
           scope: ['reporting', 'ceo'],
           state: { henry: 'The 8th' },
-          status: 'running',
+          status: 'claiming',
           taskType: 'bar',
           user: 'dabo',
           ownerId: taskManagerId,
diff --git a/x-pack/plugins/task_manager/server/task_store.ts b/x-pack/plugins/task_manager/server/task_store.ts
index fbb21d154f32..ece78943d165 100644
--- a/x-pack/plugins/task_manager/server/task_store.ts
+++ b/x-pack/plugins/task_manager/server/task_store.ts
@@ -216,48 +216,39 @@ export class TaskStore {
       claimTasksByIdWithRawIds,
       size
     );
+
     const docs =
       numberOfTasksClaimed > 0
         ? await this.sweepForClaimedTasks(claimTasksByIdWithRawIds, size)
         : [];
 
-    // emit success/fail events for claimed tasks by id
-    if (claimTasksById && claimTasksById.length) {
-      const [documentsReturnedById, documentsClaimedBySchedule] = partition(docs, (doc) =>
-        claimTasksById.includes(doc.id)
-      );
-
-      const [documentsClaimedById, documentsRequestedButNotClaimed] = partition(
-        documentsReturnedById,
-        // we filter the schduled tasks down by status is 'claiming' in the esearch,
-        // but we do not apply this limitation on tasks claimed by ID so that we can
-        // provide more detailed error messages when we fail to claim them
-        (doc) => doc.status === TaskStatus.Claiming
-      );
-
-      const documentsRequestedButNotReturned = difference(
-        claimTasksById,
-        map(documentsReturnedById, 'id')
-      );
+    const [documentsReturnedById, documentsClaimedBySchedule] = partition(docs, (doc) =>
+      claimTasksById.includes(doc.id)
+    );
 
-      this.emitEvents(
-        [...documentsClaimedById, ...documentsClaimedBySchedule].map((doc) =>
-          asTaskClaimEvent(doc.id, asOk(doc))
-        )
-      );
+    const [documentsClaimedById, documentsRequestedButNotClaimed] = partition(
+      documentsReturnedById,
+      // we filter the schduled tasks down by status is 'claiming' in the esearch,
+      // but we do not apply this limitation on tasks claimed by ID so that we can
+      // provide more detailed error messages when we fail to claim them
+      (doc) => doc.status === TaskStatus.Claiming
+    );
 
-      this.emitEvents(
-        documentsRequestedButNotClaimed.map((doc) => asTaskClaimEvent(doc.id, asErr(some(doc))))
-      );
+    const documentsRequestedButNotReturned = difference(
+      claimTasksById,
+      map(documentsReturnedById, 'id')
+    );
 
-      this.emitEvents(
-        documentsRequestedButNotReturned.map((id) => asTaskClaimEvent(id, asErr(none)))
-      );
-    }
+    this.emitEvents([
+      ...documentsClaimedById.map((doc) => asTaskClaimEvent(doc.id, asOk(doc))),
+      ...documentsClaimedBySchedule.map((doc) => asTaskClaimEvent(doc.id, asOk(doc))),
+      ...documentsRequestedButNotClaimed.map((doc) => asTaskClaimEvent(doc.id, asErr(some(doc)))),
+      ...documentsRequestedButNotReturned.map((id) => asTaskClaimEvent(id, asErr(none))),
+    ]);
 
     return {
-      claimedTasks: numberOfTasksClaimed,
-      docs,
+      claimedTasks: documentsClaimedById.length + documentsClaimedBySchedule.length,
+      docs: docs.filter((doc) => doc.status === TaskStatus.Claiming),
     };
   };
 
diff --git a/x-pack/test/plugin_api_integration/test_suites/task_manager/task_manager_integration.js b/x-pack/test/plugin_api_integration/test_suites/task_manager/task_manager_integration.js
index ea95eb42dd6f..c87a5039360b 100644
--- a/x-pack/test/plugin_api_integration/test_suites/task_manager/task_manager_integration.js
+++ b/x-pack/test/plugin_api_integration/test_suites/task_manager/task_manager_integration.js
@@ -28,8 +28,7 @@ export default function ({ getService }) {
   const testHistoryIndex = '.kibana_task_manager_test_result';
   const supertest = supertestAsPromised(url.format(config.get('servers.kibana')));
 
-  // FLAKY: https://github.com/elastic/kibana/issues/71390
-  describe.skip('scheduling and running tasks', () => {
+  describe('scheduling and running tasks', () => {
     beforeEach(
       async () => await supertest.delete('/api/sample_tasks').set('kbn-xsrf', 'xxx').expect(200)
     );