diff --git a/pkg/jobs/jobs.go b/pkg/jobs/jobs.go
index 38484b13be1d..df50e1e30771 100644
--- a/pkg/jobs/jobs.go
+++ b/pkg/jobs/jobs.go
@@ -145,6 +145,18 @@ func (j *Job) CheckStatus(ctx context.Context) error {
 	})
 }
 
+// CheckTerminalStatus returns true if the job is in a terminal status.
+func (j *Job) CheckTerminalStatus(ctx context.Context) bool {
+	err := j.Update(ctx, func(_ *client.Txn, md JobMetadata, _ *JobUpdater) error {
+		if !md.Status.Terminal() {
+			return &InvalidStatusError{md.ID, md.Status, "checking that job status is success", md.Payload.Error}
+		}
+		return nil
+	})
+
+	return err == nil
+}
+
 // RunningStatus updates the detailed status of a job currently in progress.
 // It sets the job's RunningStatus field to the value returned by runningStatusFn
 // and persists runningStatusFn's modifications to the job's details, if any.
diff --git a/pkg/sql/logictest/testdata/logic_test/schema_change_in_txn b/pkg/sql/logictest/testdata/logic_test/schema_change_in_txn
index c15cde27543a..b2ce5a18224d 100644
--- a/pkg/sql/logictest/testdata/logic_test/schema_change_in_txn
+++ b/pkg/sql/logictest/testdata/logic_test/schema_change_in_txn
@@ -1720,3 +1720,25 @@ DROP INDEX b_idx CASCADE;
 
 statement ok
 COMMIT;
+
+# Test that deleting an index on a table that gets dropped in the same
+# transaction is allowed.
+subtest delete_index_and_table_in_txn
+
+statement ok
+CREATE TABLE people (id INT PRIMARY KEY, name STRING);
+
+statement ok
+CREATE INDEX people_name_index ON people (name);
+
+statement ok
+BEGIN;
+
+statement ok
+DROP INDEX people@people_name_index;
+
+statement ok
+DROP TABLE people;
+
+statement ok
+COMMIT;
diff --git a/pkg/sql/schema_changer.go b/pkg/sql/schema_changer.go
index c9b7ae9a35c9..7d14ef822d03 100644
--- a/pkg/sql/schema_changer.go
+++ b/pkg/sql/schema_changer.go
@@ -1315,17 +1315,24 @@ func (sc *SchemaChanger) done(ctx context.Context) (*sqlbase.ImmutableTableDescr
 	}
 
 	descs, err := sc.leaseMgr.PublishMultiple(ctx, tableIDsToUpdate, update, func(txn *client.Txn) error {
-		if jobSucceeded {
-			if err := sc.job.WithTxn(txn).Succeeded(ctx, jobs.NoopFn); err != nil {
-				return errors.Wrapf(err,
-					"failed to mark job %d as successful", errors.Safe(*sc.job.ID()))
-			}
-		} else {
-			if err := sc.job.WithTxn(txn).RunningStatus(ctx, func(ctx context.Context, details jobspb.Details) (jobs.RunningStatus, error) {
-				return RunningStatusWaitingGC, nil
-			}); err != nil {
-				return errors.Wrapf(err,
-					"failed to update running status of job %d", errors.Safe(*sc.job.ID()))
+		// If the job already has a terminal status, we shouldn't need to update
+		// its status again. One way this may happen is when a table is dropped
+		// all jobs that mutate that table are marked successful. So if is a job
+		// that mutates a table that is dropped in the same txn, then it will
+		// already be successful. These jobs don't need their status to be updated.
+		if !sc.job.WithTxn(txn).CheckTerminalStatus(ctx) {
+			if jobSucceeded {
+				if err := sc.job.WithTxn(txn).Succeeded(ctx, jobs.NoopFn); err != nil {
+					return errors.Wrapf(err,
+						"failed to mark job %d as successful", errors.Safe(*sc.job.ID()))
+				}
+			} else {
+				if err := sc.job.WithTxn(txn).RunningStatus(ctx, func(ctx context.Context, details jobspb.Details) (jobs.RunningStatus, error) {
+					return RunningStatusWaitingGC, nil
+				}); err != nil {
+					return errors.Wrapf(err,
+						"failed to update running status of job %d", errors.Safe(*sc.job.ID()))
+				}
 			}
 		}