diff --git a/pgconn.go b/pgconn.go
index 5644904a..50607095 100644
--- a/pgconn.go
+++ b/pgconn.go
@@ -1435,12 +1435,17 @@ func (rr *ResultReader) receiveMessage() (msg pgproto3.BackendMessage, err error
 }
 
 func (rr *ResultReader) concludeCommand(commandTag CommandTag, err error) {
+	// Keep the first error that is recorded. Store the error before checking if the command is already concluded to
+	// allow for receiving an error after CommandComplete but before ReadyForQuery.
+	if err != nil && rr.err == nil {
+		rr.err = err
+	}
+
 	if rr.commandConcluded {
 		return
 	}
 
 	rr.commandTag = commandTag
-	rr.err = err
 	rr.rowValues = nil
 	rr.commandConcluded = true
 }
diff --git a/pgconn_test.go b/pgconn_test.go
index 6362c51b..379aa266 100644
--- a/pgconn_test.go
+++ b/pgconn_test.go
@@ -1752,6 +1752,71 @@ func TestConnCloseWhileCancellableQueryInProgress(t *testing.T) {
 	pgConn.Close(closeCtx)
 }
 
+// https://github.com/jackc/pgx/issues/800
+func TestFatalErrorReceivedAfterCommandComplete(t *testing.T) {
+	t.Parallel()
+
+	steps := pgmock.AcceptUnauthenticatedConnRequestSteps()
+	steps = append(steps, pgmock.ExpectAnyMessage(&pgproto3.Parse{}))
+	steps = append(steps, pgmock.ExpectAnyMessage(&pgproto3.Bind{}))
+	steps = append(steps, pgmock.ExpectAnyMessage(&pgproto3.Describe{}))
+	steps = append(steps, pgmock.ExpectAnyMessage(&pgproto3.Execute{}))
+	steps = append(steps, pgmock.ExpectAnyMessage(&pgproto3.Sync{}))
+	steps = append(steps, pgmock.SendMessage(&pgproto3.RowDescription{Fields: []pgproto3.FieldDescription{
+		{Name: []byte("mock")},
+	}}))
+	steps = append(steps, pgmock.SendMessage(&pgproto3.CommandComplete{CommandTag: []byte("SELECT 0")}))
+	steps = append(steps, pgmock.SendMessage(&pgproto3.ErrorResponse{Severity: "FATAL", Code: "57P01"}))
+
+	script := &pgmock.Script{Steps: steps}
+
+	ln, err := net.Listen("tcp", "127.0.0.1:")
+	require.NoError(t, err)
+	defer ln.Close()
+
+	serverErrChan := make(chan error, 1)
+	go func() {
+		defer close(serverErrChan)
+
+		conn, err := ln.Accept()
+		if err != nil {
+			serverErrChan <- err
+			return
+		}
+		defer conn.Close()
+
+		err = conn.SetDeadline(time.Now().Add(5 * time.Second))
+		if err != nil {
+			serverErrChan <- err
+			return
+		}
+
+		err = script.Run(pgproto3.NewBackend(pgproto3.NewChunkReader(conn), conn))
+		if err != nil {
+			serverErrChan <- err
+			return
+		}
+	}()
+
+	parts := strings.Split(ln.Addr().String(), ":")
+	host := parts[0]
+	port := parts[1]
+	connStr := fmt.Sprintf("sslmode=disable host=%s port=%s", host, port)
+
+	ctx, cancel := context.WithTimeout(context.Background(), 5*time.Second)
+	defer cancel()
+	conn, err := pgconn.Connect(ctx, connStr)
+	require.NoError(t, err)
+
+	rr := conn.ExecParams(ctx, "mocked...", nil, nil, nil, nil)
+
+	for rr.NextRow() {
+	}
+
+	_, err = rr.Close()
+	require.Error(t, err)
+}
+
 func Example() {
 	pgConn, err := pgconn.Connect(context.Background(), os.Getenv("PGX_TEST_CONN_STRING"))
 	if err != nil {