Miami pulled away in the third period, getting a season-best 25 points from Jermaine O'Neal and 23 from Richardson. It was Miami's fifth win in six games, the last two victories coming to open a six-game homestand.
Dwyane Wade contributed 22 points and Mario Chalmers had 17 for the Heat.
Chicago, which has lost seven in a row, got 20 points each from James Johnson and Jannero Pargo.
With the game deadlocked early in the third, Miami embarked on a 19-7 run and eventually took a 12-point advantage into the final period. The Heat enjoyed an 11-0 surge in the fourth quarter.
Miami has defeated Chicago five straight times.