James Johnson had 17 points off the bench for Miami, which both scored and allowed its most points all season to register its first back-to-back wins.
"It's a huge game for us," said Dragic, whose team entered Saturday ranked third in the league in average points allowed. "We're not a team that runs a whole lot. ... But we just need to grind. And we did that tonight."
Dion Waiters scored 16 points for Miami, and Josh Richardson hit four 3-pointers among his 15 points as Miami went 13 for 27 (48.1 percent) from beyond the arc. In all, six Heat players scored in double figures.
"We try to get to the paint and attack," Heat coach Erik Spoelstra said. "But teams have been really loading up on that, and so we're trying to develop some more trust, some more ball movement to make teams pay for that."
Miami shot 57.7 percent from the floor, almost 16 full points above its season average entering Saturday.
"They had some guys that usually don't make shots that made shots because they were basically workout shots -- there was nobody there to contest them," Wall said. "I think we came out with intensity. I just think our one-on-one defense was terrible."
Behind Wall and Beal, center Marcin Gortat scored 10 points and grabbed 16 rebounds. But no other Wizards hit double figures on a night Washington lost starting forward Markieff Morris to a sprained right ankle in the second quarter.
After Dragic's jumper gave Miami a 60-59 lead to end the first half, the Heat opened the third quarter on a 10-4 run, stretching their lead to 70-63 on Whiteside's bank shot.
Later in the third, Miami built its lead to 13 after a 12-4 stretch. Dragic drove inside for the last four points, his latter layup making it 89-76 with 2:41 left in the quarter.
"Man, the first half, nobody played defense," Dragic said. "But we figured it out. The third quarter was good for us."
Washington trailed by as many as 17 in the fourth, before closing the game on a 10-1 run. That was a little deceiving, with Wall's second 3-pointer in that stretch coming with 0.9 seconds left.
Heat: Improved to 3-0 when scoring 100 or more points ... Waiters started after testing a minor groin injury in pregame warm-ups ... F Willie Reed left early in the second quarter with a hyperextended right knee.
Wizards: Sank to 1-8 when opponents score 100 or more points, and 3-5 in games when both Wall and Beal start. ... C Ian Mahinmi (knee surgery) will participate in his first practice of the season Sunday. ... Morris said he expects to practice Sunday.
BOARDS IN BUNCHES
Whiteside extended his season-opening, double-digit rebound streak to 12 games despite waiting until 3:34 left in the second quarter to pick up his first. By halftime, he had six.
"He's a monster," Dragic said.
A SECOND HOME
With the victory, Miami is now 24-14 all-time at the Verizon Center. Its .632 winning percentage here is its highest at an opponent's building where it has played at least 15 games.
Heat: Open a four-game season series against the 76ers in Philadelphia on Monday.
Wizards: Close a three-game homestand against Phoenix on Monday.
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