Zingari-Richmond was competitive for 40 minutes but numerous holes opened up in its defence in the second spell at Miller Park.
Green Island led just 7-0 at the break but added four more tries in the second spell.
The midfield combination of Sam Erepia and Chris O'Neill cut holes in the Zingari defence, and flanker Jason Bint and hooker Ricky Hollamby had strong games in the pack.
No 8 Chris Bell and lock Brady Carmichael were the best of the Zingari forwards.
Green Island 34 (Chris O'Neill 2, Sam Erepia, Paul Butson, Josh Beer tries; Shane McNoe pen, 3 con), Zingari-Richmond 0.
Halftime: Green Island 7-0.
Referee: Doug Rodgers.
