Green Island blasted to a 17-0 lead in the first five minutes but then took its foot off the accelerator and allowed Zingari-Richmond back into the game at Miller Park.
Powerful No 8 Junior Sala had an outstanding game and made the break for both of Green Island's tries.
He was difficult to stop and had the ability to break the advantage line and set up scoring opportunities for his backs.
The first try came after just 30 seconds when halfback Dean Moeahu capitalised on Sala's break by scooting up the left flank for 40m.
Talented fullback Buxton Popoalii used his pace to add the second try and Green Island looked set for a cricket score.
But Zingari rallied and took control in the forwards, with towering lock Tom Rowe dominating the lineout. He made eight clean takes. No 8 Andrew Melville added oomph to the scrum.
Strong tackling by flanker Chris Bell shut down the Green Island attacks and hooker Shota Horie was lively around the paddock.
Zingari's first try came after 28 minutes when Rowe claimed the lineout inside the 22m and first five-eighth Christian Walker broke through.
The strong Zingari scrum was the foundation for the second try seven minutes later when fullback Nathan Napier scored after two phases.
Both sides cancelled each other out in a second spell punctuated by handling mistakes and players choosing wrong options.
Other Green Island players to impress were lock Josh Beer with his covering tackles and first five-eighth Joe Bartlett, who kicked four goals from his six attempts.
Walker played soundly at first five-eighth for Zingari and speedy fullback Nathan Napier added spark on the counter-attack and was safe under the high ball.
Green Island 20 (Buxton Popoalii, Dean Moeahu tries; Joe Bartlett 2 con, 2 pen), Zingari-Richmond 17 (Nathan Napier, Christian Walker tries; Walker 2 con, pen). Halftime: 17-14.
