diff --git a/batch.go b/batch.go
index 0e86fead..8f6ea4f0 100644
--- a/batch.go
+++ b/batch.go
@@ -139,7 +139,10 @@ func (br *batchResults) Exec() (pgconn.CommandTag, error) {
 	}
 
 	commandTag, err := br.mrr.ResultReader().Close()
-	br.err = err
+	if err != nil {
+		br.err = err
+		br.mrr.Close()
+	}
 
 	if br.conn.batchTracer != nil {
 		br.conn.batchTracer.TraceBatchQuery(br.ctx, br.conn, TraceBatchQueryData{
diff --git a/batch_test.go b/batch_test.go
index f65b018e..44abbd8e 100644
--- a/batch_test.go
+++ b/batch_test.go
@@ -742,6 +742,27 @@ func TestSendBatchErrorWhileReadingResultsWithoutCallback(t *testing.T) {
 	})
 }
 
+func TestSendBatchErrorWhileReadingResultsWithExecWhereSomeRowsAreReturned(t *testing.T) {
+	t.Parallel()
+
+	pgxtest.RunWithQueryExecModes(context.Background(), t, defaultConnTestRunner, nil, func(ctx context.Context, t testing.TB, conn *pgx.Conn) {
+		batch := &pgx.Batch{}
+		batch.Queue("select 4 / n from generate_series(-2, 2) n")
+
+		batchResult := conn.SendBatch(ctx, batch)
+
+		_, execErr := batchResult.Exec()
+		require.Error(t, execErr)
+
+		closeErr := batchResult.Close()
+		require.Equal(t, execErr, closeErr)
+
+		// Try to use the connection.
+		_, err := conn.Exec(ctx, "select 1")
+		require.NoError(t, err)
+	})
+}
+
 func TestConnBeginBatchDeferredError(t *testing.T) {
 	t.Parallel()