They were undeterred -- and wound up dealing Miami a fairly severe blow.
John Salmons scored 17 points before leaving late in the game with a head gash that needed 12 stitches, Luc Richard Mbah a Moute added 14 points and 12 rebounds, and the Bucks beat the Heat 90-85 about an hour or so after Milwaukee was eliminated from playoff contention.
"We knew sooner or later that was going to come, but that lets you know where we stand as a team -- as competitors also," Bucks forward Drew Gooden said.
The Bucks only trailed for 9 minutes, 46 seconds against the Heat, who were 3-0 against Milwaukee this season.
And just because the Bucks are out doesn't mean they won't have a say in the Eastern Conference race: They knocked the Heat a half-game back of Boston in the chase for the No. 2 seed in the Eastern Conference.
"Nobody said this was going to be easy," Heat coach Erik Spoelstra said.
Even if Miami (54-24) wins its final four games, it will need the Celtics to lose at least twice in order to pass them in the standings. Boston holds the tiebreaker over the Heat by having won all three meetings this season; the fourth is Sunday in Miami.
Miami shot only 41 percent, and its 16 turnovers led to 18 Milwaukee points.
"Every time you play them, it's going to be one of those grind-it-out tough games," James said. "They make it very physical. ... I've played against Scott Skiles teams when he was in Chicago and now in Milwaukee, and it's always the same effort."
The Bucks were officially eliminated when Indiana beat Washington. The Pacers wrapped up the last available East postseason spot later Wednesday when Orlando topped Charlotte in overtime.
So the Bucks became spoilers, and played the role to perfection.
"You don't want to take anything away from it," Skiles said. "The reality is that we got eliminated tonight."
The fifth and final lead change came with 2:27 left, when Delfino hit a 3-pointer for an 81-79 lead.
With the Milwaukee lead at four, James scored the next three Miami points, but the Heat lost a chance to take the lead when Mike Bibby was called for an illegal screen with 41 seconds left. Delfino's third 3-pointer came 17 seconds later, dooming Miami.
"It was a shot that they gave me and I've got confidence from all of my teammates, the coaches and everybody," Delfino said. "And I just made it."
Down by as many as 14 in the first half, Miami got within one with 3:56 remaining until intermission on a dunk by Joel Anthony. Milwaukee scored the next four points, making it 45-40.
It stayed that way for about 30 minutes, in real time anyway.
Neither team scored in the final 2:45 of the half -- the Bucks were 0 for 6 in that span, Miami 0 for 5. After the break, James ended the drought with an 18-footer with 11:02 left in the third.
Milwaukee's drought lasted another 1:33, snapped only when Delfino beat the shot clock with a 3-pointer that put the Bucks up 48-44. That was a theme for much of the night: When the Heat had a chance to take the lead, they usually came up empty, including on seven such possessions in the second and third quarters.
Then in the fourth, Miami shot 7 for 21, with Bosh missing six of his nine shots, James four of his six. Perhaps illustrating how much they missed Wade, the starting Heat backcourt on Wednesday of Bibby and James Jones not only didn't score in the fourth quarter, but didn't even attempt a shot.
"You have to give credit to their defense," Bosh said. "They play good defense. ... Things are going to happen like that sometimes."
Skiles pointed to the large high-definition video board hanging over midcourt in the first quarter, trying to plead his case that referees had botched a foul call. "HD nowadays. That's not a foul," Skiles said, to no avail. ... Mike Miller and Anthony became Miami's first pair of reserves to grab 10 or more rebounds in the same game since Matt Geiger and Rony Seikaly did it against the Clippers on Jan. 8, 1994. ... Mbah a Moute tipped a rebound into the Heat basket in the first quarter. Erick Dampier was credited with the score.
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