One night after the Heat played Oklahoma City, Miami's two stars played only the first quarter. James scored 12 points and Bosh had two before spending the rest of the game in sweatsuits.
The third leg of Miami's Big Three, Dwyane Wade, sat out his second straight game with a sore right hamstring.
Patrick Beverley had 11 points and 10 rebounds for the Heat.
James, who signed with the Heat over the summer after seven seasons in Cleveland, got a mix of cheers and boos from the sellout crowd before the game. One woman held up a "LeBron Marry Me?" sign.
Once the action started, James scored 12 of the Heat's 26 points in the first quarter. Bosh, who scored 23 the night before, had a rough start. Blair went over him for San Antonio's first basket and Bosh missed five of his six shots in the quarter.
James and Bosh played the entire period. Wade, who sat on the bench in a warm-up suit, was the first to offer handshakes at the break.
While the lineup of James, Bosh and Wade has made the Heat a favorite for the NBA championship, there's nothing new about San Antonio's Big Three of Tim Duncan, Manu Ginobili and Tony Parker.
The Spurs also sat their stars for long stretches. Ginobili played 10 minutes of the first quarter, but Duncan logged only seven minutes and didn't play after the period. When a relaxed Duncan leaned on the media table to stretch, he waved to two schoolgirls who called his name, bringing a squeal from the young fans.
James Jones put Miami up 46-40 when he was fouled on a 3-pointer and made the free throw. Then Ginobili and Parker showed they've still got some magic when Ginobili fired a bullet pass to Parker, who finished the play with a reverse scoop layup to trim Miami's lead to four at halftime.
Duncan was on the floor with Parker and Ginobili to start the third, but coach Gregg Popovich pulled him for Antonio McDyess a split second before the whistle to start play. The Spurs opened things up with an 18-2 run capped by Curtis Jerrells' long jumper that made it 63-53.
The Spurs outscored Miami 20-10 in the fourth. Miami committed 19 turnovers.
Richard Jefferson and Jerrells each scored 11 for San Antonio.
Jones added 12 points for Miami.