Brian Cook's 3-pointer with 51.5 seconds remaining gave the Wizards a 95-93 lead, and Beal, the former Florida star drafted third overall, made two free throws with 5.5 seconds left to seal the victory.
Cook and Jordan Crawford also scored 14 points apiece for Washington.
Tristan Thompson had 18 points and 10 rebounds to lead Cleveland.
Kyrie Irving, the rookie of the year last season, scored nine points on 3-of-13 shooting in 25 minutes. Irving is 11 of 46 from the field in four preseason games.
The Wizards were playing without several players, including star point guard John Wall, who is expected to be out until December with a knee injury. Emeka Okafor (stomach virus), Greg Booker (hamstring),Nene (foot) and Chris Singleton (shoulder) also missed the game.
J.R. Smith drains a 3-pointer from deep in the first quarter against the Raptors.
Bismack Biyombo drains a jumper early in the first quarter against the Cavs.
Minnesota Timberwolves point guard Ricky Rubio's mother has died after a long battle with lung cancer.