The last three Golden State wins have come to open a seven-game road trip. The Warriors handed Miami its third home loss of the season.
Curry scored 36 points and handed out 12 assists. Lee grabbed 14 rebounds to go with his 32 points.
Golden State shot 56 percent from the field, hit 15-of-29 from 3-point range and outrebounded the Heat by nine.
Klay Thompson added 16 points for Golden State and Harrison Barnes had 15.