It was Simmons' sixth triple-double of the season, the most by a rookie since 1991-92.
An off-balance shot by JJ Redick with 20 seconds left gave the 76ers a 102-99 lead. Miami had a chance to tie, but Wayne Ellington missed a pressured 3-point attempt with 16 seconds left.
Miami's Dwyane Wade missed a 3-point try at the buzzer that would've won the game. Wade's shot from the top of the key hit the front rim and the backboard before falling off.
Philadelphia won without All-Star center Joel Embiid, who missed the game due to a sore right ankle, a problem that surfaced earlier this week. The 76ers improved to 3-8 without Embiid. Dario Saric led the 76ers with 19 points, and newly acquired Marco Belinelli added 17.
The 76ers have won nine consecutive home games, their longest streak since 2008.
Philadelphia, the top rebounding team in the NBA, grabbed 23 offensive boards -- the most allowed by Miami all season.
The Heat were led by reserve forward James Johnson, who scored 22 points. Center Hassan Whiteside produced his fifth consecutive double-double with 16 points and 10 rebounds.
Miami All-Star point guard Goran Dragic scored 18 points but just two after halftime.
The Heat dropped their fifth straight road game. Miami is just 5-11 in its past 16 games and 1-7 in its past eight. The Heat have lost twice at Philadelphia in the past two weeks.
Philadelphia, which entered the game four games over .500 for the first time in six years, won its fifth consecutive game overall.
Miami got off to a good start, leading 29-20 after the first quarter. The Heat extended their lead to 62-39 at halftime, shooting 52.4 percent in the first 24 minutes. Miami had a 32-22 edge in paint points and held the Sixers to 34 percent shooting.
Philadelphia stormed back in the third quarter, cutting its deficit from 24 points to eight at 81-73.
The 76ers, which had not led since 9-7 in the first quarter, didn't lead again until a Simmons alley-oop bucket gave them a 92-90 advantage.
Miami wound up shooting 45.5 percent from the field to Philadelphia's 42.4 percent. However, the 76ers posted a massive 60-29 rebounding edge.
--Field Level Media