Marcelo Montoya opened the scoring for the Auckland-based side in the 16th minute before the Bunnies hit back with tries to Alex Johnston and Cameron Murray to lead 12-6 at halftime.
South Sydney pulled away in the second half, Johnston grabbing his second, Tyrone Munro scoring on debut and Blake Taaffe dotting down in the 78th minute to seal a hard-fought 28-6 win.
The Warriors have not beaten the Rabbitohs since 2018.