Bosh scored 13 of his 23 points in the first half, when Miami trailed 27-21 after the first quarter.
"I just made an effort to get to the basket a little more," he said. "We just kept wearing on them offensively. They made some tough shots."
Los Angeles shot 42 percent in its third straight loss. The Lakers were 14 of 36 from 3-point range as they tried to go over the top to beat the Heat's rugged interior.
"Teams will try to get us moving and play out of our rotations," Heat coach Eric Spoelstra said. "Early on they were getting some wide-open ones. Some of those Nick Young hit were tough."
Jordan Farmar returned from a left hamstring tear after missing 10 games, giving the Lakers a true point guard to run the offense. But he was ineffective, with three points and two assists in 32 minutes.
"I hadn't even played 5-on-5 since I got hurt, so this is the first time I've actually played basketball," he said. "Health-wise, everything stayed intact and I felt good out there, so it's progress."
The Lakers played a competitive game against the loaded Heat despite their poor shooting and the absence of Bryant, Steve Nash (nerve root irritation) and Steve Blake (right elbow). They led by 10 points and never trailed by more than that.
"I thought we attacked them the way we wanted to," Lakers coach Mike D'Antoni said. "We can step it up a bit and be a little bit tougher, especially on the boards and places like that. Those things are irritating, but the effort is good."
Young's basket tied the game for the last time at 83-all. The Heat promptly took off on a 13-5 run. Wade, Norris Cole and James scored all of the Heat's points.
Young answered with his fourth 3-pointer of the game and Meeks made 1 of 2 free throws to pull the Lakers to 96-92 with 1:26 to play. But Wade had an acrobatic reverse layup and James made two foul shots to give Miami some breathing room.