The Cavaliers are 31/20 to win at home and force a deciding Game 7.
Golden State moved a win away from winning its first championship since 1975 after defeating Cleveland 104-91 at the Oracle Arena last Sunday.
Curry (5/7 to win Finals MVP) scored 17 of his 37 points in the fourth period to lead the Warriors. The reigning league MVP also got plenty of support from his teammates.
Draymond Green had 16 points, nine rebounds and six assists while Andre Iguodala tallied 14 points, eight rebounds and seven assists. Leandro Barbosa provided the spark off the bench with 13 points while Klay Thompson had 12.
LeBron James paced the Cavaliers with 40 points, 14 rebounds and 11 assists while Tristan Thompson had 19 points and 10 rebounds.
JR Smith added 14 points but did not score in the second half. Timofey Mozgov was also a non-factor as the Russian center failed to score after posting a career-high 28 points in Game 4.