Curry was just 3 of 12 from 3-point range, but scored a game-high 26 points in the 115-113 win on Monday at Staples Center in Los Angeles.
The Warriors trailed 92-81 at the start of the final frame. They went on to outscore the Lakers 34-21 over the final 12 minutes and used a 15-2 run to take the lead with 2:40 remaining.
"We don't want to get in those positions, but we just have to keep fighting and see what happens," Curry told reporters.
Kelly Oubre Jr. had 23 points for the Warriors. Eric Paschall scored 19 points off the Golden State bench. Andrew Wiggins also scored 18 points in the win.
"We know we can play much better," James said. "You learn from all of it and apply it to the next game."
The Warriors (7-6) host the San Antonio Spurs at 10 p.m. EST on Wednesday at Chase Center in San Francisco. The Lakers (11-4) battle the Milwaukee Bucks at 7 p.m. EST on Thursday at Fiserv Forum in Milwaukee.