Gino Padula put Rangers ahead before Miller equalised and was then dismissed for a second bookable offence in a frenzied five minute spell.
Miller was booked shortly before Padula's 72nd minute free kick from the right sailed past the goalkeeper Steve Phillips and into the far corner of the net.
Rangers were pegged back within two minutes. The ball broke to Miller inside the area and he smashed past goalkeeper Chris Day.
But Miller had barely finished his goal celebrations when he foolishly tripped Marc Bircham off the ball when City were in possession, and was ordered off by referee Phil Prosser.
In the 18th minute, Martin Rowlands' 30-yard free kick bounced back off the post and nine minutes before half time, Paul Furlong's long-range drive struck the bar.
City always looked a threat and went close when Christian Roberts sent a right footed shot wide and when Brian Tinnion missed the target with a curling effort.
Miller's leveller, scored just as QPR seemed to be on their way to victory, was the first goal Rangers have conceded at Loftus Road this season.
The home side were unable to make their extra man count after Miller walked, and City almost nicked the second goal when Luke Wilkshire hit the top of the bar with a free kick.
Furlong had a great chance at the death but Phillips denied him with a fine double save at the far post.
Rangers manager Ian Holloway felt his side threw away two points: "When you score against a team you have to really strangle the life out of them but we didn't do that.
"We allowed our concentration to slip and we went from being on a high to on a low because we allowed them back into the game when we should have killed them off."
QPR: Day; Edghill (Ainsworth), Forbes, Gnohere, Padula; Rowlands, Bircham, Bean (Oli), McLeod (Palmer); Gallen, Furlong.
Subs not used: Culkin, Sabin.
City: Phillips; Woodman, Coles, Butler, Bell; Wilkshire, Doherty, Tinnion, A Brown; Miller, Roberts (Lita).
Subs not used: Stowell, Hill, Burnell, Hulbert