Curry was 1 of 7 from 3-point range before starting overtime with back-to-back 3-pointers to give the Warriors a 115-109 lead. He shot 5 of 6 from the free-throw line in the final 1:14 to hold off Los Angeles.
Draymond Green had 15 points, 11 rebounds and nine assists, and Zaza Pachulia matched his season high with 11 points for the Warriors.
The score was tied 84-84 to start the fourth quarter and was knotted nine more times in the fourth, the last on Durant's 3-pointer with 46 seconds left, but both teams missed their final shots of regulation.
Lakers point guard Lonzo Ball scored eight consecutive points in the third quarter as Los Angeles went from four points down to four points ahead, but neither team could sustain a run.
Ball finished with 15 points and 10 assists.
The Lakers shot 12 of 16 in the second quarter and closed with an 18-4 run to take a 54-50 lead into the locker room.
Ingram scored 14 points in the first half and Randle had 12.
The Warriors committed five of their 22 turnovers in the first four minutes of the game but still managed to lead by as many as 11 in the first quarter.
Golden State took a 30-20 lead into the second quarter and led by 10 four other times in the quarter before Ingram made a 3-pointer with 4:15 left in the first half to spark the 18-4 run.
Randle made the 10th consecutive field goal for Los Angeles to stretch the advantage to 54-50.
The Lakers played without leading scorer Kyle Kuzma, who was ruled out after experiencing back spasms during warmups. Kuzma, a rookie forward out of Utah, is averaging 16.7 points, 6.1 rebounds and shooting 50.4 percent from the floor.
NOTES: Lakers F Kyle Kuzma started 11 games at power forward while Larry Nance Jr. recovered from a fracture in his left hand and averaged 16.8 points as a starter. Kuzma had moved back to the bench in a 120-115 loss to the Los Angeles Clippers on Monday. Nance finished with no points in 22 minutes against the Warriors. ... The Lakers ranked last in the NBA in 3-point shooting at 31.3 percent, and the Warriors were second at 39.7 percent through Tuesday. The Lakers shot 9 for 34 (37.5) from 3-point distance for the game, and Golden State shot 12 for 30 (40 percent). ... Golden State came in leading the NBA at 30.1 assists a game. The Warriors finished with 30 assists Wednesday.