David Lee had 26 points and nine rebounds and Klay Thompson scored 22 points for the Warriors, who built an 18-point lead early in the fourth quarter before the Suns surged back.
Gerald Green had 25 points and six rebounds, and Goran Dragic added 24 points and six assists for the Suns, who dropped into a tie with Memphis for eighth place in the crowded Western Conference standings.
Golden State is 9-2 since the All-Star break and a season-high 16 games over .500. The Warriors are two games ahead of Dallas for sixth in the West.
Neither team showed much playoff poise in the final minute.
Green's layup cut Golden State's lead to 111-107 with 38.1 seconds remaining. After Thompson missed a 3-pointer, Andre Iguodala came down with a rebound and the Suns were forced to foul.
Phoenix caught a break when Iguodala missed both free throws. But then Green stepped out of bounds receiving a pass from Dragic on the sideline.
Steve Blake missed two free throws to give the Suns yet another chance. Phoenix followed that up with Marcus Morris air-balling a 3-pointer, and Iguodala made two free throws to seal Golden State's victory.
The Suns also missed a chance to take the four-game season series over the Warriors — and the potential head-to-head tiebreaker for playoff seeding that comes with it. Each team won both meetings on its home floor.
The Warriors outshot Phoenix 52.9 percent to 48 percent. The Suns outrebounded Golden State 41 to 35 but committed 20 turnovers, while the Warriors only had 12.
With a nagging quad limiting his playing time, Curry shook off the pain and made sure coach Mark Jackson kept him on the court longer than expected. Curry made a 3-pointer and handed out six assists during a 23-4 run in the third quarter, and the Warriors went ahead 96-78 early in the fourth.
Curry shot 7 for 16 from the floor in 30 minutes. He said before the game that he injured his quad during Golden State's win at Boston on Wednesday and began to feel pain again during Friday's victory over Atlanta.
Both Jackson and Curry said they will communicate with each other during games to determine when — and how much — the All-Star point guard plays.
While he looked a step slow defending Dragic, Curry came through when his team needed him most.
After the Suns went ahead by 12 in the second quarter, Curry converted a reverse layup while getting fouled by Morris to start a three-point play that brought the Warriors within one. But back-to-back 3-pointers by Dragic helped Phoenix carry a 61-56 lead into intermission.
The Warriors disrupted Phoenix's offense in the third quarter by trapping Dragic at half court. The swarming defense led to several fast-break opportunities, and Curry controlled the offense with near perfection to put the Warriors ahead for good.
NOTES: Suns coach Jeff Hornacek said G Eric Bledsoe, who has been out since Dec. 30 recovering from knee surgery, will likely return for Wednesday's home game against Cleveland. Hornacek said there's a chance Bledsoe could play Monday night at the Los Angeles Clippers. ... The Warriors recalled G Nemanja Nedovic from Santa Cruz Warriors of the NBA Development League. ... Suns C Miles Plumlee had two points and four rebounds in 11 minutes after missing the two previous games because of a sprained shoulder.