Green had not scored more than 20 in a game during the 2012-13 campaign, but he delivered 31 against the Suns. He hit 11-of-14 shots from the field to go with seven rebounds.
For the first time this season the Celtics won a road game against a Western Conference opponent.
Goran Dragic scored 19 points for Phoenix, which has dropped six out of seven.
Florida bear attack: Black bear mauls woman's face
Toddler uninjured after being knocked over by Obama family dog