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.
For the Roosters, they came back to earth with a thud after a promising win over Newcastle last week.
A brilliant Latrell Mitchell try opened the scoring in the third minute.
However, it was one-way traffic thereafter in front of a crowd of 14,493 at Allianz Stadium, more than half of whom seemed to be Warriors supporters.
The Warriors big men laid the platform, with Stephen Kearney's side running for 1345m compared with the Roosters' 834m.
And Green put the icing on the cake.
While Roosters halves Luke Keary and Cooper Cronk - whose night was summed up when he kicked out on the full - had shockers, Green steered his side around the park brilliantly.
It was a performance that would have surely made NSW selectors take notice.
Despite missing Johnson, the Warriors looked slick and assured with the ball in hand.
All three of their first-half tries came off set plays as they led 18-6 at the break.
Tohu Harris stood and offloaded for Lino's four-pointer before back-rower Leivaha Pulu ran a neat line to give his side the lead in the 17th.
The only try of the second half came when Lino put in an inch-perfect bomb for David Fusitua.