Curry overcame a poor shooting performance after halftime, and nearly recorded a triple-double by adding 11 assists and nine rebounds. Curry was just 2 of 12 from the floor in the second half and OT.
David Lee scored 19 before fouling out for the Warriors, who are on the road for seven games over the next 13 days.
Kyrie Irving scored 27 for Cleveland, which dropped its fifth straight and lost its third tight game in a row. The Cavs lost by three in Boston on Saturday and two in double-overtime against Atlanta on Thursday.