Goneva, who had earlier scored a try for the Fijians in a pulsating second half after the game had been locked at 7-7 at halftime, was sinbinned for a deliberate knockdown while attempting an intercept with just over 10 minutes remaining.
Takulua’s penalty, his second within the space of three minutes, gave the Tongans a 20-19 lead they extended when Faleafa crossed two minutes later.
Tonga had led 14-7 shortly after halftime when lock Steve Mafi crossed but the Fijians struck back through Goneva and lock Viliame Mata to take a 19-14 lead into the final quarter.
Tonga hooker Paula Ngauamo and Fiji scrumhalf Frank Lomani had scored tries in the first half to leave the match locked at halftime.
Samoa were not involved for this weekend’s international matches due to their World Cup qualifying playoff against Germany next Saturday in Apia.
The second match of the inter-continental playoff is in Germany on July 14 with the winner qualifying directly for the World Cup in Japan and completing Pool A with the hosts, Ireland, Russia and Scotland.
The loser goes into a four-team repechage tournament in November to determine the final qualifier. (Reporting by Greg Stutchbury in Wellington; Editing by Amlan Chakraborty)