Yet even with all that, it ultimately took overtime before the Heat finally could put away the Milwaukee Bucks 113-106 Wednesday night at AmericanAirlines Arena, in a true Big Three effort.
"Obviously, we got off to a great start. We really imposed our will," Heat coach Erik Spoelstra said. "And from there we just relaxed.
"It's got to be more about our consistency."
Instead, it was about star power, what the Heat had and the Bucks lacked.
Wade and LeBron James each scored 28 points, with Chris Bosh adding 24 points and 18 rebounds, his high as a member of the Heat. James again wound up approaching a triple-double, adding 10 rebounds and eight assists.
"Same old story," James joked of yet being unable to complete a triple-double this season. "It's not even surprising at this point."What was surprising was how the Heat had to push through the finish of regulation, and beyond.
"Some of 'em are ugly," Bosh said. "We play a lot of games. We have to be satisfied. We can't be disappointed and win on the same night."
Haslem, in particular, wanted to make sure it was not a night of mixed emotions.
"It would have put a dark cloud over the whole moment if we didn't win the game," he said of passing Mourning for the franchise's all-time rebounding lead, with a video presentation at the end of the first quarter following his milestone moment and teammates offering a, "One! Two! Three! U.D.!" in the locker room afterward.
"Now," he said. "I can celebrate."
The Big Three made sure of that.
The game was tied 98-98 entering overtime, with Wade converting a long jumper to put the Heat up 100-98. A give-and-go from Wade to James then staked the Heat to a 102-98 edge. A pair of Bosh free throws put the Heat up 104-98, effectively ending it.
"We had to earn it," Spoelstra said.
Wade had a chance to end it in regulation off an inbounds play with 1.4 seconds left, but his twisting attempt was cleanly blocked by Bucks guard Monta Ellis, moments after Ellis was off with a jumper on the other end.
"I just wanted to come back and be aggressive and be in the rhythm I'd been in," Wade said, pleased with this step toward that goal.
When Scott Skiles is the opposing coach, be it with the Chicago Bulls or currently with the Bucks, it rarely has been easy for the Heat.
It certainly wasn't this time, with the Bucks pushing all the way back from those early deficits to a 73-71 lead entering the fourth quarter.
But with Wade back on his game there still was enough to push through for what now is a perfect 5-0 start to the season at AmericanAirlines Arena.
With Wade, James and Bosh stepping up, the Heat survived a 13-0 Bucks run late in the second quarter and Samuel Dalembert 's first career 3-pointer, a heave that beat the halftime buzzer and completed a 16-2 quarter-ending surge.
Opening a run of 10 of 11 at home, the Heat fed off the crowd early, fell asleep after building their 37-19 lead, and then found a way to extend their overall winning streak to three, with Haslem closing with eight rebounds on his milestone night, the second giving him the franchise career rebounding record.
With a little late 3-point help from Ray Allen, normalcy eventually was restored, with Allen closing with 17 points.
It appeared it would be easier with Bucks guard Brandon Jennings and Ellis combining to miss their first 10 shots. Jennings came around to close with 19 points, but Ellis finished 4 of 16 for nine.
"They're a veteran team and closed out the game," Ellis said.