diff --git a/call.go b/call.go
index 13c8b821..32ca7eb3 100644
--- a/call.go
+++ b/call.go
@@ -147,7 +147,7 @@ func Invoke(ctx context.Context, method string, args, reply proto.Message, cc *C
 				// This was a retry; return the error from the last attempt.
 				return toRPCErr(lastErr)
 			}
-			return Errorf(codes.Internal, "%v", err)
+			return toRPCErr(err)
 		}
 		stream, err = sendRPC(ctx, callHdr, t, args, topts)
 		if err != nil {
diff --git a/test/end2end_test.go b/test/end2end_test.go
index 504e7f6f..4b3c1db6 100644
--- a/test/end2end_test.go
+++ b/test/end2end_test.go
@@ -301,6 +301,18 @@ func setUp(useTLS bool, maxStream uint32) (s *grpc.Server, tc testpb.TestService
 	return
 }
 
+func TestTimeoutOnDeadServer(t *testing.T) {
+	s, tc := setUp(false, math.MaxUint32)
+	s.Stop()
+	// Set -1 as the timeout to make sure if transportMonitor gets error
+	// notification in time the failure path of the 1st invoke of
+	// ClientConn.wait hits the deadline exceeded error.
+	ctx, _ := context.WithTimeout(context.Background(), -1)
+	if _, err := tc.EmptyCall(ctx, &testpb.Empty{}); grpc.Code(err) != codes.DeadlineExceeded {
+		t.Fatalf("TestService/EmptyCall(%v, _) = _, error %v, want _, error code: %d", ctx, err, codes.DeadlineExceeded)
+	}
+}
+
 func TestEmptyUnary(t *testing.T) {
 	s, tc := setUp(true, math.MaxUint32)
 	defer s.Stop()