The Heat overcame a late six-point deficit to defeat a San Antonio team that competed without four players, including veteran center Tim Duncan, who were sent home for an extra day's rest.
San Antonio was playing its sixth game in nine days -- all on the road. Miami, meanwhile, had not played since Saturday.
Duncan, Manu Ginobili, Tony Parker and Danny Green all were excused from the game by Coach Gregg Popovich. The coach said he made the decision when the 2012-13 schedule was released and he saw the difficult November road his team would have to travel.
NBA Commissioner David Stern, however, rejected the idea that the Spurs could decide which players to use in which games.
He issued a statement prior to the game apologizing to the fans.
"This is an unacceptable decision by the San Antonio Spurs and substantial sanctions will be forthcoming," the statement said.
San Antonio won the first five games of the road trip and came very close to defeating the defending NBA champions Thursday.
The Spurs had a 95-89 lead with 3 minutes to play, but Miami climbed to within one on Dwyane Wade's layup with 1:02 remaining.
Gary Neal then missed a 3-point attempt for the Spurs and Allen put the Heat in front at 100-98 by hitting a 3-pointer with 23 seconds left.
LeBron James scored 23 points to lead the Heat with Allen producing 20 and Wade 19.
Neal had 20 points for the Spurs, who came into the game with a 9-1 record on the road and a league-high 13 victories. Tiago Splitter, getting the start at center in place of Duncan, had 18.