But until they do, the Bulls will have to settle for finding ways to pull victories out in dramatic fashion.
The Bulls (13-10) led by as many as 13 points in the third quarter. But the Heat cut the deficit to 101-100 with less than a minute before Butler hit four free throws down the stretch to cap the win.
The Heat (7-17) played for the last shot in trying to set up a game-tying 3-point field goal, but turned the ball over when they mishandled a handoff. Miami was forced to foul Butler, who capped the win with two free throws with less than a second to play.
It wasn't exactly artistic, but in Wade's words, a win is a win.
"In this league, there's going to be some nights when you're going to play amazing, there's going to be some nights when you don't play well and there's going to be some nights when you play just good enough to get a win," said Wade, who also had three assists and a steal. "Never begrudge a win. We played good enough to get a win tonight."
The Bulls hung on despite watching the Heat all but wipe out the double-digit lead Chicago built in the third quarter when Wade scored 11 of his 28 points. Miami (7-17) lost its fifth straight game a night after losing by 30 points to the Cleveland Cavaliers.
Goran Dragic scored 21 points and had 11 assists to lead the Heat. Whiteside, who was benched Friday night for a lack of energy, scored Miami's first eight points and finished with 20 points and rebounds.
Despite getting close, though, the Heat found themselves without the benefit of a timeout and couldn't set up a play for a potential game-tying shot.
"It was a tough few possessions down the stretch," Whiteside said. "We wish it went another way, but sometimes, it doesn't go that way."
Added Heat coach Erik Spoelstra: "It's just tough for it to come down to a play like that to decide the game."
The Heat, who played their fourth game in five days, also got 15 points from Tyler Johnson off the bench, 11 from Josh Richardson and 10 from Derrick Williams in the loss.
Wade, playing for the second time against his team he spent the first 13 seasons of his career with, proved to be a difference-maker. The veteran guard sparked the Bulls into the fourth quarter when Hoiberg said his team dropped its head a bit after Miami made its move. But behind Wade and Butler, the Bulls did just enough.
"We will get better," Hoiberg said, "but I'm glad we got this win tonight."
Robin Lopez also had 10 rebounds for Chicago, which has won back-to-back games after losing three straight.
The Bulls surpassed the 100-point mark despite connecting on one 3-point field goal. But Chicago got to the free-throw line 31 times, hitting 28, and rode Wade's energy to the win.
"Dwyane obviously had it going tonight," Hoiberg said. "I thought he had a lot of pop."
Despite pulling out the victory, both Wade and Hoiberg admitted the Bulls still have plenty of work to do to become a more consistent team, especially down the stretch. But Wade, for one, won't complain about results like Saturday's.
"We are a team that can any game, we can lose any game," he said. "We have shown that throughout the year. Right now, I am focused on our two-game winning streak."
NOTES: Heat C Hassan Whiteside played through knee and hip ailments as the Heat continue to deal with injuries. ... G Josh Richardson (sprained ankle) played in a reserve role against the Bulls and appeared in a game for the first time since Nov. 28. Richardson was one of five players the Heat left in Miami before departing for a three-game road trip. "That's much needed to have him around," coach Erik Spoelstra said. ... F Udonis Haslem returned to the lineup after being excused for missing Friday's game against Cleveland to see his son play in a Florida high school football state championship game. ... Bulls G Dwyane Wade faced his former team for the second time since leaving Miami. Wade stopped at the Heat locker room before the game, which Spoelstra said remains awkward. "That's not ever going to look right -- him in a Bulls uniform," Spoelstra said.