Toronto guard Kyle Lowry added 25 points, including five in in the final minute as the Raptors held off a late Heat rally.
The Raptors surged at the start and led by as many as 16 points in the first quarter and were ahead by 20 in the second quarter before the Heat began chipping away.
The Raptors took a 13-point lead into the fourth quarter, and Miami reduced it to five with just under five minutes to play.
The margin was down to one after Dwyane Wade, who had a team-high 20 points for Miami, converted two free throws with 1:54 to play.
DeRozan made two free throws with 1:33 left, and Toronto led by three points.
Miami turned the ball over on its next possession, and Lowry, who added 10 rebounds and six assists, hit a 3-pointer with 52.5 seconds to play to give Toronto a 93-87 edge.
Wade's shot cut the lead to four before Lowry answered with a jumper to restore the six-point lead with 23.7 seconds remaining.
A goaltending call on Wade's shot with 21.7 seconds to go moved Miami within four points.
DeRozan made two free throws with 21.3 seconds left and made two more with nine seconds remaining to increase the lead to eight points and clinch the win.
Bismack Biyombo added 10 points and six rebounds for Toronto.
Goran Dragic and Josh Richardson each scored 13 points for the Heat, and Joe Johnson added 11 points and eight rebounds.
The Raptors stormed out to a 16-point lead during the first quarter. With DeRozan scoring 10 points and Lowry adding nine, Toronto led 28-18 after the opening quarter. The Heat shot 27 percent from the field in the period, and Toronto shot 40 percent.
The Heat crept to within eight of the Raptors early in the second quarter, but when Lowry made a driving reverse layup with 3:39 to play in the half, Toronto led by 20 points. The Heat then reeled off 10 straight points, six by Dragic. Toronto led 55-45 at the half.
Lowry scored 16 first-half points, and DeRozan and Biyombo added 10 each. Dragic led Miami with 10 first-half points.
Wade started the second half with a 3-pointer to reduce the Miami deficit to seven points.
DeRozan then scored six consecutive points to give Toronto a 13-point lead during a stretch in which Miami was twice called for 24-second violations.
Raptors forward DeMarre Carroll was helped off the court with an injury with 1:16 to play in the third quarter after crashing to the floor beneath Toronto's offensive basket. He walked past the bench to the dressing room.
Carroll, who had six points, six rebounds and four personal fouls in 26 minutes, did not return.
The Raptors led 75-62 after the third quarter.
The Heat whittled the lead to eight points before DeRozan's jumper and free throw restored the 13-point lead with 8:33 to play in the fourth quarter.
DeRozan picked up his fifth personal foul with 8:19 to play.
Richardson hit a pair of 3-pointers to trim the lead to seven.
Justise Winslow cut the lead to five points with a jumper with 4:44 left.
After a Lowry miss with just under three minutes to play, Wade cut the lead to three points with a step-back jumper.
