Shaquille O'Neal shook off a deep thigh bruise to add 17 points and 11 rebounds in 32 minutes for the Heat, but Miami did not need a big performance from their big star to take the opening game of the best-of-seven series.
Game Two is in Miami on Tuesday.
The Heat had two players score more than 30 points in a single playoff game for the first time in franchise history thanks to Wade and Jones.
The duo were sharp with their shooting as O'Neal worked his way slowly back into the line-up after suffering the thigh injury a week ago.
Wade finished 12-for-18 from the field and added eight assists, while Jones was 10-for-12, including 7-for-9 from three-point range for Miami.
Udonis Haslem added 11 points and had 11 rebounds for the Heat, the heavy favourites over the eighth-seeded Nets, who needed 15 wins in their final 19 games just to make the playoffs.
Vince Carter led New Jersey with 27 points and 10 rebounds, but the Nets never got to within single-digits of Miami's lead in the second half.
Jason Kidd added 18 points for the Nets, while Travis Best, Clifford Robinson and Nenad Krstic all had 11 points for New Jersey.
All-Star forward Richard Jefferson returned to the Nets line-up after missing the final 49 games of the season with a wrist injury.
Jefferson contributed nine points in 23 minutes.
