Green had a game-high 28 points as the Warriors moved into a 2-0 series lead courtesy of the 110-77 win at the Oracle Arena on Sunday.
Stephen Curry (18 points) and Klay Thompson (17) were relatively quiet once again, but others stepped up.
Green also had seven rebounds and five assists, while Leandro Barbosa (10 points) was five-of-seven from the field off the bench.
Andrew Bogut had four blocks in the first quarter – the most in the quarter of a Finals game since Ben Wallace (five in 2005) – and finished with five.
LeBron James had 19 points, nine assists and eight rebounds for the Cavs, who were outscored heavily in every quarter except the first.
While the Warriors went at 54.3 per cent from the field, the Cavs' percentage was down at 35.4.
Kyrie Irving (10 points) and James combined to go 12-of-31 from the field.
In a further blow, they lost Kevin Love to concussion after an accidental elbow from Harrison Barnes in the second quarter.
Love played just under 21 minutes and finished with five points.
Game three of the series is in Cleveland on Wednesday, with the Cavs bidding to become just the fourth team in history to come from 2-0 down to win the Finals.