Russell Westbrook flirted with his 19th triple-double, finishing with a team-high 27 points, eight rebounds and a game-high nine assists, as the Thunder snapped a two-game losing streak.
Devin Booker poured in a game-high 30 points for the Suns, who lost their fourth in a row.
Playing for the third time on a four-game trip, Phoenix led by as many as seven points early on and retained a 36-34 lead past the midpoint of the second period.
Anthony's 3-pointer with 4:59 remaining in the period gave the Thunder a lead they never relinquished and triggered the 15-point burst that left the Suns well behind for good.
Paul George had a 3-pointer, Westbrook a jumper and Corey Brewer a pair of layups before Anthony connected from deep again, creating a 49-36 margin just 1:05 before halftime.
The Thunder went up by as many as 22 points in the third quarter before coasting home to even their record at 1-1 on their four-game homestand.
All five Oklahoma City starters scored in double figures, led by Westbrook, who made 11 of his 14 shots.
George added 21 points, Brewer 17, Steven Adams 16 and Anthony 11 for the Thunder, who were coming off a 122-112 home loss to Houston.
Brewer was making his first start for Oklahoma City after having been picked up off waivers last week.
Adams also collected a game-high 12 rebounds to complete a double-double.
Booker knocked down four 3-pointers to account for nearly half of his 30 points for the Suns, who have lost 14 of their last 15 games. He topped 20 points for the ninth consecutive game and 30 points for the 22nd time this season.
Tyson Chandler added 10 points for Phoenix, which completes its four-game trip Saturday at Charlotte.
The Suns shot just 33.7 percent for the game and hit only 9 of their 37 3-point attempts.
--Field Level Media
Phoenix | Oklahoma City | |
Devin Booker 30 | Scoring | Russell Westbrook 27 |
Elfrid Payton 6 | Assists | Russell Westbrook 9 |
Devin Booker 6 | Rebounds | Steven Adams 12 |
Devin Booker 6 | Free Throws Made | Jerami Grant 5 |
Troy Daniels 2 | Steals | Steven Adams 2 |
Tyson Chandler 1 | Blocks | Steven Adams 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Phoenix | 87 | 33.7 | 9-37 | 16-18 | 15 | 43 | 4 | 9 | 15 |
Oklahoma City | 115 | 52.5 | 13-33 | 18-27 | 21 | 49 | 11 | 6 | 18 |