Curry was 13 for 22 from the field and 8 for 15 from beyond the arc for Golden State. Lee added 14 rebounds, Klay Thompson scored 16 points and Harrison Barnes added 15 for the Warriors.
LeBron James scored 26 points and Dwyane Wade added 22 for the Heat, which had all five starters in double figures. Chris Bosh scored 19, Mario Chalmers had 17 and Shane Battier added 11 for Miami.
But the Heat allowed Golden State to shoot 56 percent, make 15 of 29 tries from 3-point range and finish with a 40-31 rebounding edge.
Curry became the first player with at least 36 points, 12 assists and eight 3-pointers in a game since Antoine Walker did it for Boston on Jan. 17, 2001. The 123 points was Golden State's second-best total of the season, two shy of what the Warriors put up on opening night against the Los Angeles Lakers, and the 15 3-pointers matched a season best.
About the only blip for the Warriors were turnovers. They had 20, which Miami turned in 32 points. Without those, this might have been a lot worse.
For a few seconds of the first quarter, the Warriors were shooting 11 for 13 for the game.
Even that wasn't good enough for the lead.
That's how much offense reigned on this night.
Somehow, the Warriors — despite shooting nearly 85 percent to that point — were trailing 29-28, part of what was a sizzling opening barrage that set the tone for the evening. Golden State scored on 14 of its first 21 possessions and led 38-33 after the opening quarter, putting up the highest point total for any period against the Heat this season.
Things cooled, albeit slightly, in the second, and the Warriors went into the break with a 65-61 advantage.
And then the third quarter was all about Curry. He was dazzling, wowing Julius Erving at one end, Johnny Manziel on the other and pretty much frustrating the Heat at all points in between.
He went on a personal 7-0 run early in the period, all of them jump shots from a total distance of 63 feet, one of them on a play where he gave a quick look-back to James after a high-arcing, high-difficulty connection from the right corner. That barrage alone gave Golden State a 13-point lead, and a 3 from Curry put the Warriors up 91-76 with 3:27 left in the quarter.
Curry had 14 in the quarter, matching his output from the entire first half. But the lead was down to nine entering the fourth, and the Heat kept chipping away, with James taking a difficult pass from Wade and scoring down low to get Miami within 105-99 with about 7½ minutes remaining.
James' 3-pointer with 5:18 left got Miami within six again. But he missed a pair of free throws with 3:16 left, Thompson found Curry with a touch pass a few seconds later — and Curry delivered his eighth 3-pointer of the night, the one that just about wrapped things up for the Warriors.
NOTES: Golden State's 123 points were the most allowed by the Heat at home in a non-overtime game since James, Wade and Bosh became teammates. ... Attendance was 20,350, tying the largest home regular-season crowd for the Heat at AmericanAirlines Arena. ... Flo Rida and Pharrell Williams were also part of the crowd. ... The only other players with at least 35 points and 12 assists against the Heat in a game: Michael Jordan and Allen Iverson, according to STATS.