Green Island may have won the penalty shoot-out but Zingari-Richmond left Miller Park with the points.
All four of Zingari's tries came from its ability to exploit frailties in the Green Island backline, with five-pointers to Chris Bell, Kurt Schruder, Johnny Noakes and Tim Hanipale.
Shannon Young kept Green Island in the hunt with seven successful penalty goals from eight attempts, and the penalty count favoured Green Island 14-12.
But as the game progressed Zingari-Richmond maintained the momentum and focus through strong forward play led by lock Brady Carmichael in the set-pieces and No 8 Chris Bell in general play.
Carmichael claimed 11 clean line-out takes to help set up some enterprising back play.
For Green Island, Andre Clarke was a powerhouse in the scrum and in general play and Tamati Tamakehu displayed some brilliant touches from fullback.
Zingari-Richmond 36 (Chris Bell, Kurt Schruder, Johnny Noakes, Tim Hanipale tries; Matt Gordon 4 penalties 2 conversions)
Green Island 21 (Shannon Young 7 penalty goals).
Half-time: Zingari-Richmond 16-6.
Referee: Dave Kennedy.