"We did a pretty good job on him, but also there were some shots maybe he would normally make," coach Scott Skiles said. "So you never take too much credit when you're playing against a guy who's that good."
Wade led the Heat with 21 points, but never seemed to get into his usual dominating rhythm due to foul trouble.
Wade, who shot 6 for 20, missed the six 3-point attempts he tried, including a pair of 3s down the stretch.
"He can get his shot whenever he wants," Skiles said. "You just have to hang in and do the best you can."
Bell seemed to get the better of the matchup as Wade fouled Bell twice in the second quarter and also had an offensive foul.
Brandon Jennings, who scored 17 points and had five assists, liked how Bell guarded Wade.
"I guess we got the D-Wade stopper on the team right now," Jennings said. "He did a real good job, but I think everybody did a good job showing help."
The two teams meet in Miami on Monday.
Wade said that his back was problematic, especially coming after back-to-back games.
"It was tight, but no doubt, I was able to play," he said after playing about 31 minutes. "The only thing I can do now is, hopefully, get some rest tomorrow. Hopefully, Monday, I'll be back. I'll be able to have my explosiveness back going to the basket."
Andrew Bogut scored 17 points and grabbed 15 rebounds for Milwaukee which improved to 6-0 at the Bradley Center in 2010.
The Heat were without forward Michael Beasley, their second-leading scorer, and guard Mario Chalmers. Beasley missed his second consecutive game with a hyperextended right knee. Chalmers sprained his left thumb when he got it caught in a jersey Friday night against the Detroit Pistons.
The Bucks led from early in the first quarter, pushed the margin to 18 in the second and then held a comfortable double-digit lead through the third. Miami finally got under 10 points early in the fourth quarter when a basket by Daequan Cook and a jumper by Carlos Arroyo pulled the Heat to 71-63 with 9:59 left.
Delfino, who had 16 points, answered for Milwaukee with two free throws and Warrick tipped in a shot as Milwaukee regained a double-digit lead at 75-63.
Wade, with five fouls, came back with 7:24 to go and the Bucks leading 79-65, but it wasn't enough as Warrick sank three long jumpers to keep the Bucks ahead.
The Bucks' 13-point lead thanks to Warrick, was cut to five when O'Neal dunked, Richardson and Dorell Wright each hit a 3. Miami got no closer as Jennings hit a 3-pointer. Wade missed two 3-point attempts before Jennings sealed the victory with three free throws.
"We just couldn't put the ball in the basket like we normally do," Wade said.
A bit of good news for the Heat came when O'Neal showed no lingering effects of his knee injury suffered in the first minute of the win over Detroit on Friday night.
Bogut, Warrick and Jerry Stackhouse keyed the second quarter as Milwaukee outscored Miami 33-17.
Bogut converted consecutive three-point plays before his two free throws gave the Bucks a 56-38 lead at the half. Warrick and Stackhouse, who signed a free-agent contract 13 days ago, each had eight points as a reserve as momentum seemed to swing toward the Bucks.
In the second quarter, Wade finally had enough when he complained to referee Kane Fitzgerald that he had been fouled by Bell when Wade lost the ball. Fitzgerald promptly called a technical on Wade who moments later left the game after picking up his fifth foul.
NOTE: Chalmers' streak of 128 consecutive games played ended. He is averaging 7.2 points. ... The Bucks finished the month with an 8-7 record for their first winning January since 2003-04.