Anthony finished 18 of 26 from the field, reaching 50 on a jumper with 16.9 seconds remaining.
Chris Bosh scored 23 points for Miami, which played without LeBron James, Dwyane Wade and Mario Chalmers, all held out with injuries that are not believed to be serious.
The Heat had their 17-game home winning streak snapped.
WIZARDS 90, BULLS 86
In Washington, John Wall had 27 points, nine assists and eight rebounds, Emeka Okafor scored the go-ahead dunk in the final minute and the Wizards won their eighth consecutive home game.
Wall was 8 for 17 from the field and 11 for 13 at the free throw line as the Wizards maintained pursuit of their goal of becoming the best team not to make the playoffs. They want to pass the Philadelphia 76ers and finish ninth in the Eastern Conference – not bad for a team that started 4-28 – and Tuesday’s win left them 2½ games back with eight to play.
Carlos Boozer had 19 points and 12 rebounds to lead the Bulls.