The 3 was Chalmers' 80th in the postseason, tying Tim Hardaway's franchise record.
After Luc Richard Mbah a Moute made the second of two free throws, James scored on a layup. Redick made a jumper, but Shane Battier and Allen closed out the Bucks with a pair of 3s.
James then converted a three-point play and added a layup to complete the 19-5 run — a spurt in which he had a hand in every single Miami score.
"At some point during that stretch right there, he decided he was going to put his imprint on the game and he did. In a big way," Boylan said. "When you're a superstar player like he is, that's what superstar players do."
James finished with 30 points, eight rebounds and seven assists. Allen finished with 16, going 4 of 7 from 3-point range.
Dunleavy had 17 points and Redick 10. But the Bucks got almost nothing again from Jennings, who didn't even play in the fourth quarter. He finished with three points on 1-of-7 shooting.
After scoring 26 points in Game 1, Jennings had 27 total in the final three.
"Frustrated, a little down because I came into this season with so much confidence," Jennings said. "I thought we had a chance to steal a game in Game 1, Game 2. We let that slip away from us. Game 3, we came back home. Had a 10-point lead, lost that. I mean it's frustration all around."
And now, uncertainty.
"I feel like Milwaukee is doing something now, trying to make a tradition of being a playoff team," Sanders said. "This is our first step."
NOTES: The Heat have won eight straight postseason games dating back to last season. That matches the franchise record. ... NBA Commissioner David Stern was in attendance. ... James scored 30 or more for the 54th time in the postseason, second only to Kobe Bryant among active players. ... Milwaukee had seven of its 16 turnovers in the first quarter. ... The Bucks are now 20-26 in elimination games. ... Packers LB Clay Matthews was at the game.