The superstar went up high for two blocks on 7-footer Brook Lopez, including one in overtime, and swatted a jumper by Vince Carter into the stands in the final minute of regulation. Wade's 3-point play with 37.2 seconds left in overtime stretched Miami's lead to eight at 96-88.
Trailing by 16 points in the first quarter, the Heat rode a season-high 19 points from Yakhouba Diawara and 17 points from Michael Beasley. Miami's biggest previous comeback was Dec. 22 against Indiana, when it rallied from 15 points down.
New Jersey cut it to 99-96, but Carter's desperation 3-point attempt missed.
Keyon Dooling had 23 points, and Carter had 20 for the Nets, who won in overtime a night earlier against the Atlanta Hawks.
Both teams took big blows before the game even began.
Devin Harris, who leads New Jersey in scoring and assists, was resting a sore right hamstring and was inactive against Miami. And Heat forward Shawn Marion had back spasms and was a late scratch.
The rest of the starters would fill in fine.
Wade missed a jumper from just inside the arc as the fourth quarter buzzer sounded.
Wade had given the Heat an 85-83 lead on a pair of free throws, but Dooling hit a runner in the lane to tie it at 85 with 8.4 seconds left.
Notes: Heat coach Erik Spoelstra said before the game that center Alonzo Mourning will decide if he will return in the next 3-4 weeks. Mourning, who still has a locker in the Heat dressing room, is rehabbing and has said he hopes to re-sign with Miami sometime this season. ... Harris also was sidelined for New Jersey's only other trip this year to Miami on Nov. 10, when the Heat won 99-94. ... The Heat, playing their second game in as many nights, improved to 2-5 in the second half of back-to-back games. ... Wade went into the locker room at the end of the third quarter with a bruised left knee but quickly returned.