Chris Wilcox had 13 points off the bench, and Avery Bradley and Jason Terry scored 13 each for the Celtics, who moved two games ahead of Milwaukee for seventh place in the Eastern Conference.
Green started in place of 36-year-old Kevin Garnett, given a rest with Boston playing its third game in four nights. Green responded by going 11 of 14 from the floor and setting his season high for points.
Paul Pierce scored only eight on 3-of-5 shooting for his fourth single-digit game of the season. But that mattered little to the Celtics, who were dominant from the opening tip in snapping a two-game skid.
Jordan Crawford, acquired from Washington on Thursday, made his Celtics debut and scored 10 points off the bench as Boston improved to 9-3 without injured guard Rajon Rondo.
Goran Dragic had 18 points and 10 assists, Markieff Morris scored 11 and Marcin Gortat added 10 points and six rebounds for the Suns, who have lost two straight and six of seven.
Boston wasted no time taking control of the game, taking advantage of Phoenix's 0-for-5 start from the floor and a pair of Suns turnovers to open a 13-0 lead just under 4 minutes into the game.
Phoenix slowly cut into the lead, but every time the Suns came close the Celtics ran their lead back to double digits.
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The Suns' last run came in the first 2 minutes of the second half, a 7-0 streak capped by a 3-pointer from Dragic that cut Boston's 12-point halftime lead to 53-48.
But the Celtics pulled away for good, opening a 74-59 lead on Terrence Williams' layup with 3:03 left in the third quarter.
Boston, which swept the season series against Phoenix for the first time since 2008-09, led by as many as 28 in the fourth quarter.
NOTES: Boston won for the first time in eight road games against Western Conference teams. ... Suns C Hamed Haddadi, who came to Phoenix from Toronto with a second-round pick for Sebastian Telfair on Thursday, arrived midway through the first quarter but did not dress. ... At one point in the fourth quarter, the Suns had three point guards on the floor. ... Markieff and Marcus Morris became the second twin teammates in NBA history. The other set, Dick and Tom Van Arsdale, also played for the Suns and celebrated their 70th birthday on Friday. Marcus, traded from Houston on Thursday for a second-round pick, made his debut with 6:32 to play, joining Markieff on the floor for the first time since March 26, 2011, when they played for Kansas.
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