Durant narrowly missed a triple-double with 29 points, 11 rebounds and eight assists for the Warriors, who snapped a three-game home losing streak, their longest since January of 2014.
The Suns lost their 15th straight despite 22-point efforts from Marquese Chriss and Josh Jackson.
The Suns (19-59), who have two fewer wins than any other team in the NBA, led by as many as 14 points in the first half despite playing without their top two scorers (Devin Booker and T.J. Warren) and top two rebounders (Tyson Chandler and Alex Len).
But the Warriors, playing once again without injured Stephen Curry, rallied within 59-58 at halftime and then led 71-69 with 6:46 remaining in the third quarter before their explosion.
Cook (seven points), Durant (five) and Green (five) did all the scoring during the back-breaking run, which put the Suns in an 88-71 hole with 2:18 to go in the third.
Cook, Durant and Green all finished with three 3-pointers, while Klay Thompson and Nick Young buried two apiece, as Golden State made 13 of 28 (46.4 percent) from beyond the arc.
Thompson totaled 23 points, Cook 19 and Green 13 for the Warriors (56-21), who are battling Toronto (55-21) and Boston (53-23) for the second-best record in the league behind Houston (62-15).
Green dished out a game-high 12 assists to complete a double-double on a night when Steve Kerr recorded his 263rd win, tying him with Eddie Gottlieb for third place on the Warriors' all-time list behind Don Nelson (422) and Al Attles (394).
Dragan Bender had a double-double for the Suns with 14 points and a game-high-tying 11 rebounds, while Tyler Ulis had a team-high eight assists to complement 12 points.
Danuel House added a career-best 16 points for the Suns, who lost for the 14th straight time to the Warriors overall and 13th time in a row in Oakland.
--Field Level Media
Phoenix | Golden State | |
Marquese Chriss 22 | Scoring | Kevin Durant 29 |
Tyler Ulis 9 | Assists | Draymond Green 12 |
Dragan Bender 10 | Rebounds | Kevin Durant 11 |
Marquese Chriss 3 | Free Throws Made | Quinn Cook 2 |
Josh Jackson 2 | Steals | Quinn Cook 3 |
Danuel House 2 | Blocks | Kevin Durant 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Phoenix | 107 | 45.6 | 11-31 | 14-16 | 26 | 42 | 4 | 8 | 15 |
Golden State | 117 | 53.9 | 13-28 | 8-9 | 31 | 45 | 7 | 10 | 15 |