The Heat blew a 16-point first-half lead, then rallied from a 12-point second-half deficit to win their sixth straight overall and 12th straight at home -- plus get within one game of Washington in the Southeast Division.
Gilbert Arenas scored 33 for the Wizards, including three free throws with 3.1 seconds left that tied the game. Antawn Jamison had a 26-point, 15-rebound effort for Washington, which lost at the buzzer for the second straight night when Haslem went to his right and scored the game-winner.
Washington, which was out of timeouts, never got a desperation shot off before the final horn.
Alonzo Mourning had 16 points and Shaquille O'Neal -- limited to 17 minutes by foul trouble -- had 12 points for the Heat, while Haslem had 11 points and 10 rebounds. Jason Williams and Antoine Walker each had 11 points and James Posey added 10 for Miami, which hadn't had eight players reach double figures since Feb. 14, 1991.
"You can't ask for more balance than that," Heat coach Pat Riley said.
Brendan Haywood had 12 points for the Wizards.
Miami went up 104-101 with 4.1 seconds left, when Williams hit the first of two free throws. He missed the second -- the Heat went 10-for-25 from the line -- and that gave Washington a chance.
The Wizards, naturally, went to Arenas, who was fouled by Payton in the right corner with 3.1 seconds left. Arenas hit all three, tying the game, but giving Miami more than enough time.
The Heat went to Haslem, and the Miami native came through to keep the Heat's resurgence going.
"We just wanted to get a look at it," Riley said. "And Udonis got a look at it. He made a Dwyane Wade shot ... just a great shot."
Washington misfired on earlier last-second opportunities. Caron Butler was called for setting an illegal screen on Payton with 4.9 seconds left -- taking the ball out of Arenas' hands.
With 38.6 seconds left, Arenas -- who was 12-for-12 at the line beforehand -- missed the first of two free throws and only brought Washington within 103-101.
Miami led 28-14 after the opening quarter, forcing Washington into 10 straight missed shots over a six-minute stretch -- and building that edge despite O'Neal being limited to only two minutes because of foul trouble.
Payton hit his first four shots, including a 3-pointer with 10:01 left in the half to stake Miami to a 33-18 lead. The margin hit 56-40 when Walker connected on a 3-pointer with 32 seconds left.
But Arenas jumped past Dorell Wright and hit a running 3-pointer at the horn, cutting Miami's lead to 13 at the break -- and breathing life into the Wizards, who lost on a buzzer-beating 3-pointer by the New York Knicks' Steve Francis on Saturday night.
That shot started what became a 40-12 run by Washington, which shot 72 percent in the third quarter while holding the Heat to a 30 percent clip in that period. Butler's dunk with 2:13 left in the third put the Wizards up 80-68, but Miami clawed its way back.
The Wizards are 8-30 all-time in Miami. ... Payton's previous season-high was 16 at New Jersey in November.