Beasley scored 14 of his 22 points in the final period, and his late spurt gave the Heat a six-point lead. Atlanta failed to score on five consecutive possessions in the last three minutes, committing three consecutive turnovers during the stretch.
Wade made four 3-pointers, hit 14 of 18 free throws and added 10 assists. Quentin Richardson sank five 3-pointers and scored 22 points for Miami.
By halftime, the Heat were down three players. Rafer Alston wasn't at the arena for personal reasons, Dorell Wright sat out with a swollen left knee, and Jermaine O'Neal tweaked his left knee in the second quarter and missed the rest of the game.
Their absences failed to foil the unpredictable Heat, coming off an overtime victory Thursday against the Lakers. The Heat won their third game in a row, snapped the Hawks' four-game winning streak and took the season series 3-1.
Jamal Crawford scored 24 points and Joe Johnson 20 for Atlanta.
The start of the fourth quarter was delayed eight minutes after the scoreboard showed Miami leading 176-77, and then it appeared the Hawks might pull away. Crawford converted a four-point play to put them up 84-80 with 8:42 left.
But when Atlanta went cold down the stretch, the Heat took advantage. Wade made a steal and fed Beasley for a dunk that put Miami ahead to stay, 93-92 with 1:51 left. The Hawks twice missed shots, and Beasley hit a follow. Josh Smith missed for the Hawks, and Beasley sank a 3-pointer for a 98-92 lead with 47 seconds to go.
Wade kept the Heat close much of the night. With him on the bench, Atlanta outscored Miami 10-3 early in the second quarter. Six points by Joe Smith during the stretch helped the Hawks build a 37-25 lead.
Wade came into the game shooting 29 percent from 3-point range, but he sank a pair of 3-pointers in the final minute of the first half, including a 38-footer at the buzzer, to cut the margin to 56-52.
With the Heat trailing 68-56, Wade again rallied the Heat. He hit 3-pointers on consecutive possessions to cut Atlanta's lead to 68-64. He hit a dunk, and then came his back-to-back breakaways to make it 70-all.
NOTES: Wright is expected to return Tuesday at Charlotte. ... The Hawks came into the game averaging 11.9 turnovers, best in the NBA. ... F Udonis Haslem played in his 500th game for Miami, second in franchise history to Alonzo Mourning's 593. ... No difference: The Heat are 12-13 with Alston starting at point guard, 9-7 with Carlos Arroyo and 11-11 with Mario Chalmers.