diff --git a/pkg/sql/executor.go b/pkg/sql/executor.go
index 3f06dc089efd..59ad8b7c0fb3 100644
--- a/pkg/sql/executor.go
+++ b/pkg/sql/executor.go
@@ -1813,7 +1813,20 @@ func (e *Executor) execStmtInOpenTxn(
 		// statements outside of a transaction are run synchronously with mocked
 		// results, which has the same effect as running asynchronously but
 		// immediately blocking.
-		err = e.execStmtInParallel(stmt, p, res)
+		err = func() error {
+			cols, err := e.execStmtInParallel(stmt, p)
+			if err != nil {
+				return err
+			}
+			// Produce mocked out results for the query - the "zero value" of the
+			// statement's result type:
+			// - tree.Rows -> an empty set of rows
+			// - tree.RowsAffected -> zero rows affected
+			if err := initStatementResult(res, stmt, cols); err != nil {
+				return err
+			}
+			return res.CloseResult()
+		}()
 	} else {
 		p.autoCommit = txnState.implicitTxn && !e.cfg.TestingKnobs.DisableAutoCommit
 		err = e.execStmt(stmt, p, automaticRetryCount, res)
@@ -2123,16 +2136,16 @@ func (e *Executor) shouldUseDistSQL(planner *planner, plan planNode) (bool, erro
 }
 
 // initStatementResult initializes res according to a query.
-func initStatementResult(res StatementResult, stmt Statement, plan planNode) error {
+//
+// cols represents the columns of the result rows. Should be nil if
+// stmt.AST.StatementType() != tree.Rows.
+func initStatementResult(res StatementResult, stmt Statement, cols sqlbase.ResultColumns) error {
 	stmtAst := stmt.AST
 	res.BeginResult(stmtAst)
-	if stmtAst.StatementType() == tree.Rows {
-		columns := planColumns(plan)
-		res.SetColumns(columns)
-		for _, c := range columns {
-			if err := checkResultType(c.Typ); err != nil {
-				return err
-			}
+	res.SetColumns(cols)
+	for _, c := range cols {
+		if err := checkResultType(c.Typ); err != nil {
+			return err
 		}
 	}
 	return nil
@@ -2155,7 +2168,11 @@ func (e *Executor) execStmt(
 
 	defer plan.Close(ctx)
 
-	err = initStatementResult(res, stmt, plan)
+	var cols sqlbase.ResultColumns
+	if stmt.AST.StatementType() == tree.Rows {
+		cols = planColumns(plan)
+	}
+	err = initStatementResult(res, stmt, cols)
 	if err != nil {
 		return err
 	}
@@ -2189,18 +2206,20 @@ func (e *Executor) execStmt(
 	return res.CloseResult()
 }
 
-// execStmtInParallel executes the statement asynchronously and writes mocked
-// out results to res. These mocked out results will be the "zero value"
-// of the statement's result type:
-// - tree.Rows -> an empty set of rows
-// - tree.RowsAffected -> zero rows affected
+// execStmtInParallel executes a query asynchronously: the query will wait for
+// all other currently executing async queries which are not independent, and
+// then it will run.
+// Async queries don't produce results (apart from errors). Note that planning
+// needs to be done synchronously because it's needed by the query dependency
+// analysis.
+// A list of columns is returned for purposes of initializing the statement
+// results. This will be nil if the query's result is of type "RowsAffected".
 //
 // TODO(nvanbenschoten): We do not currently support parallelizing distributed SQL
 // queries, so this method can only be used with classical SQL.
-// TODO(andrei): the mocking of results business should be done by the caller.
 func (e *Executor) execStmtInParallel(
-	stmt Statement, planner *planner, res StatementResult,
-) (retErr error) {
+	stmt Statement, planner *planner,
+) (sqlbase.ResultColumns, error) {
 	session := planner.session
 	ctx := session.Ctx()
 	params := runParams{
@@ -2211,12 +2230,11 @@ func (e *Executor) execStmtInParallel(
 
 	plan, err := planner.makePlan(ctx, stmt)
 	if err != nil {
-		return err
+		return nil, err
 	}
-
-	err = initStatementResult(res, stmt, plan)
-	if err != nil {
-		return err
+	var cols sqlbase.ResultColumns
+	if stmt.AST.StatementType() == tree.Rows {
+		cols = planColumns(plan)
 	}
 
 	// This ensures we don't unintentionally clean up the queryMeta object when we
@@ -2227,7 +2245,7 @@ func (e *Executor) execStmtInParallel(
 		// TODO(andrei): this should really be a result writer implementation that
 		// does nothing.
 		bufferedWriter := newBufferedWriter(session.makeBoundAccount())
-		err := initStatementResult(bufferedWriter, stmt, plan)
+		err := initStatementResult(bufferedWriter, stmt, cols)
 		if err != nil {
 			return err
 		}
@@ -2249,10 +2267,10 @@ func (e *Executor) execStmtInParallel(
 		session.removeActiveQuery(stmt.queryID)
 		return err
 	}); err != nil {
-		return err
+		return nil, err
 	}
 
-	return res.CloseResult()
+	return cols, nil
 }
 
 // updateStmtCounts updates metrics for the number of times the different types of SQL