Wade came off the bench to score 15 of Miami's final 17 points, including the tough 18-footer over 76ers rookie Ben Simmons.
Philadelphia's JJ Redick had a chance for the win but missed a three-pointer from the top of the key at the buzzer.
It was just Miami's third win in its past 11 games.
Joel Embiid led Philadelphia with 23 points, and Dario Saric added 21 points. The 76ers have lost two in a row following a seven-game win streak.
Miami point guard Goran Dragic had 21 points, and teammate Hassan Whiteside had 15 points and a game-high 11 rebounds.
Heat reserve guard Wayne Ellington, one of the best three-point shooters in the NBA, suffered a left-leg injury in the first half and did not return. He finished with two points in 11 minutes.
In the third quarter, Heat starting guard Tyler Johnson suffered a bruised left knee, and he left the game with 16 points.
Those injuries were somewhat negated by the return of two injured Heat players. Forward Rodney McGruder, who suffered a stress fracture in his left leg in a preseason game, made his 2017-2018 debut and scored three points.
Heat power forward Kelly Olynyk, who missed the past six games due to a sprained left shoulder, returned and scored nine points.
Philadelphia led 24-17 after the first quarter, closing the period on a 9-0 run.
The Heat appeared frustrated, shooting just 31.8 percent in the quarter. Heat coach Erik Spoelstra was hit with a technical foul when he argued that a blocked shot by Embiid on a Wade layup should've been ruled goaltending.
Neither team shot that well - Philadelphia's percentage stood at 37 percent. The teams combined to make just 1 of 15 three-pointers attempts, and Embiid was the only player to hit one from deep. He made three jumpers and had a quarter-high seven points.
In the second quarter, Philadelphia extended its lead to 13 points. But Miami used a 15-0 run to get back in the game. A four-point play JJ Redick swung the momentum back to Philadelphia, and the 76ers went into halftime with a 48-45 lead.
Both teams shot under 40 percent for the first half, and the high scorers were Embiid and Dragic, each with 13 points.
In the third quarter, Philadelphia put together a 9-2 run during which Saric scored all nine points. But Miami clawed back with a Wade three-pointer at the buzzer, cutting its deficit to 75-73 entering the fourth quarter.
For the game, Miami shot 44.4 percent from the floor. The 76ers shot 41.7 percent.
--Field Level Media
Philadelphia | Miami | |
Joel Embiid 23 | Scoring | Dwyane Wade 27 |
Ben Simmons 6 | Assists | Goran Dragic 5 |
Joel Embiid 8 | Rebounds | Hassan Whiteside 11 |
JJ Redick 5 | Free Throws Made | Dwyane Wade 5 |
Robert Covington 3 | Steals | Josh Richardson 4 |
Richaun Holmes 2 | Blocks | Hassan Whiteside 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Philadelphia | 101 | 41.7 | 12-31 | 19-23 | 25 | 44 | 3 | 10 | 23 |
Miami | 102 | 43.9 | 9-27 | 21-28 | 19 | 37 | 9 | 12 | 16 |