The Warriors were dealt a massive blow when halfback Shaun Johnson was ruled out with a groin injury on the eve of the Sydney game.
In past years, such a setback would have caused the New Zealand side to put the cue in the rack but they rallied to record an important two points.
Johnson's fill-in, Mason Lino, was superb. However, Green was the chief architect as the Warriors recorded their first win without Johnson since round 22, 2014.
The Warriors are unbeaten after four rounds and look genuine contenders after six years in the finals wilderness.