The defending champions are up 2-0 in the series as they chase their third title in four years, but the scene in the best-of-seven now shifts to Cleveland for Games 3 and 4 on Wednesday and Friday, respectively.
Coming off a personal-best 51 points in a Game 1 loss, LeBron James led the Cavaliers with 29 points, but he went more than 12 consecutive minutes in the first half without a field goal, during which Golden State took the lead for good.
Curry's nine 3-pointers surpassed the single-game record of eight set by the Boston Celtics' Ray Allen in 2010.
Curry had three of his nine treys in the second quarter, during which the Warriors outscored the Cavaliers 27-18 to build a 59-46 halftime lead.
The Warriors switched defensive ace Draymond Green onto James to start the second quarter, and the ploy worked. James went from the 2:22 mark of the first quarter to the 2:16 mark of the second without a field goal.
With James (13 assists) turning his attention more to ball distribution than shooting, the Cavaliers hung within five late in the third period before Klay Thompson and David West hit 3-pointers to help re-establish a double-digit lead.
The Cavaliers never seriously threatened in the fourth quarter.
Curry hit 11 of his 26 shots and nine of his 17 3-point attempts for the Warriors, who improved to 10-1 at home in the playoffs this season.
Curry also found time for a team-high eight assists and seven rebounds.
Kevin Durant had 26 points, seven assists and a team-high nine rebounds as part of a balanced attack for Golden State, which has beaten Cleveland three consecutive years in Game 2 of the Finals.
Thompson, who was a game-time decision due to an ankle injury, finished with 20 points. JaVale McGee (12 points) and Shaun Livingston (10) gave the Warriors a surprise boost, hitting all 11 of their shots combined.
Golden State made 57.3 percent of its shots in the game.
James shot 10 of 20 from the floor. He also compiled a game-high 13 assists and missed a triple-double by one rebound, recording nine.
Kevin Love also had a double-double with 22 points and a game-high 10 rebounds for the Cavaliers, who have lost nine of their past 10 meetings with the Warriors. George Hill added 15 points for Cleveland, and Tristan Thompson scored 11.
The Cavaliers made just 41.1 percent of their field-goal attempts.
