Replacing Joakim Noah, who was bothered by an injured foot during warm-ups, Miller hit a season high in scoring and grabbed a key rebound in the closing seconds.
Derrick Rose added 20 points for the Bulls, who won their second consecutive game. Taj Gibson had 16 points and 14 rebounds.
Carl Landry came off the bench to lead Houston with 22 points. Aaron Brooks and Luis Scola each scored 20.
The Bulls led the entire game, but a late rally cut the margin to 99-97 with 1:36 to play.
Chicago missed a couple of late shots that would have put the game away, but Miller nabbed a rebound that resulted in a key jumper by Rose with 30 seconds to play.
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