Curry, who spent most of the third quarter on the bench in foul trouble, made three of his seven 3-pointers in the fourth, including two as part of a 18-8 run to close out the game.
The NBA's reigning MVP capped his night with a behind-the-back pass to Shaun Livingston for a layup that helped extend the Warriors' record home winning streak to 48 games.
Golden State (59-6) also stayed one game ahead of the pace of the 1995-96 Bulls, who set an NBA record with 72 wins.
Marreese Speights added 25 points and nine rebounds off the bench, Klay Thompson scored 20 points and Draymond Green had 19 points and six assists.
RELATED: Warriors forward Andre Iguodala out at least two weeks with sprained ankle
Phoenix (17-49) didn't go quietly.
The Suns trailed 68-58 early in the second half but stormed back to take a 95-86 lead heading into the fourth quarter.
Brandon Knight sparked Phoenix's burst with five of his career high-tying seven 3s. Knight, in his second game back after missing almost two months with a groin injury, finished with 30 points, seven assists and six rebounds.
The Warriors opened the final quarter with a 16-3 run but still trailed 108-105 with 5:50 to go.
Curry made two 3s sandwiched around a pair of dunks by Speights. Harrison Barnes then added two free throws to put Golden State up 119-108.
Alex Len and Knight scored on consecutive trips down the floor before Curry's jumper slammed the door on the Suns.
Suns: Knight had missed 21 games with a left adductor strain. . Phoenix went into the game leading the NBA with 22.6 fouls a game and was hit with 30 fouls against Golden State. . Len has 10 or more rebounds in a career-high eight straight games. The 7-1 Ukrainian had a double-double before halftime with 17 points and 10 boards. . The Suns have lost seven straight to the Warriors.
Warriors: Andre Iguodala's sprained left ankle is serious enough that the team has decided to shut down the veteran forward for the next two weeks. Iguodala, who hurt his ankle in Friday's win over Portland, will be re-evaluated then before a decision is made what to do next. "It's a big loss but we have a deep team and guys ready to step in for him," coach Steve Kerr said.
Suns: Host Minnesota on Monday.
Warriors: Host New Orleans on Monday.
Stephen Curry ignites Oracle on CSNBA https://t.co/1TQoDUNIUI— GoldenStateWarriors (@warriors) March 13, 2016
Tonight's starters: GSW - Curry, Thompson, Barnes, Green, Bogut; PHO - Knight, Booker, Tucker, Len, Chandler.— GSWStats (@gswstats) March 13, 2016