The Heat can complete the first-round sweep with another in Meadowlands in Game Four on Sunday.
If the Nets hope to advance they will have to make NBA history, no team having ever come back to win a best-of-seven playoff series after dropping the first three games.
"It wasn't pretty on either end," said Miami coach Stan Van Gundy. "We made a lot of mistakes but both teams kept battling, I'm just happy to come away with the win."
Back in New Jersey, the Nets attempted to make a stand against the heavily favoured Miami and battled the Heat to the bitter end.
Vince Carter turned in a sparkling 36-point effort and dished out 10 assists, Richard Jefferson added 23 and Jason Kidd had his eighth career playoff triple-double with 16 points, 16 rebounds and 13 assists but couldn't put away the Heat, who continued their dominance over the Nets by collecting their eighth straight win.
Back to nearly full fitness from a thigh injury, O'Neal had his best game of the series, playing 47 minutes.
The Heat got double-figure efforts from six players, Udonis Haslem contributing 14 points and 19 rebounds to the Miami cause while Eddie Jones hit for 20 points.
In Indianapolis, Reggie Miller poured in 33 point and Jermaine O'Neal nailed 21 and 11 rebounds, sparking the Indiana Pacers to a 99-76 win over the Boston Celtics and a 2-1 lead in their Eastern conference quarter-final.
Miller, who will retire after the playoffs, also had seven rebounds and was 11-for-12 from the free throw line as the Pacers regained control of the best-of-seven series with Game Four scheduled for Saturday at the Conseco Fieldhouse.
Paul Pierce had 19 points for the Celtics while Gary Payton chipped in with 15 points, eight rebounds and six assists.
Leading 26-23, Indiana stamped their authority on the contest early in the second, going on an 18-5 run to push their advantage into double figures.
The Celtics would rally in the third, trimming the Pacers lead to 67-59, got no closer, Indiana going on another 12-0 run in the fourth, keyed by seven straight points from Miller, to put the contest out of reach.
Tempers flared in the final quarter, Antoine Walker and O'Neal exchanging shoves and glares.
With just over four minutes left to play Walker was ejected from the game while O'Neal was hit with a technical foul.
"We got our tail kicked," said Boston coach Doc Rivers. "They competed harder and got all the loose balls.
"If we try to think our way through this series we are not going to do well."
In Houston, Dirk Nowitzki scored 28 points and Michael Finley added 20 as the Dallas Mavericks stopped the Houston Rockets 106-102, to get their first win of their Western conference quarter-final.
With the Rockets winning Games One and Two in Dallas, the home team is yet to register a victory in the best-of-seven series, which the Mavericks will look level at 2-2 with another triumph in Houston in Game Four on Saturday.
Jerry Stackhouse contributed 18 points to the Dallas cause while Jason Terry had 13.
Tracey McGrady had another big night for the Rockets, hitting for 28 points, nine rebounds and six assists while Bob Sura had 21 points and 11 rebounds.
Yao Ming ran into early foul trouble but still finished with the double-double, 15 points and 10 rebounds.
With no team having ever come back from a 3-0 series deficit, the Mavericks played with an intensity that was lacking in large portions of the first two games.
The Mavericks put their stamp on the game with a 17-0 run in the fourth quarter to surge in front 100-88.
"Down the stretch we made some adjustments," said Nowitzki. "I just tried to stay aggressive. For our team to be successful I have to stay aggressive and hopefully it will be the same in Game Four."