Yaya Toure's strike was the only goal of a one-sided first half, the Ivorian hammering home after Carlos Tevez's volley was blocked.
But wasteful finishing allowed QPR to level via the bandaged head of Bobby Zamora on the hour - only for Edin Dzeko to immediately restore City's lead after being set up by Tevez, who then stabbed home Dzeko's wayward shot for a third goal in stoppage time.
Norwich City left White Hart Lane with a deserved point after Robert Snodgrass struck a second-half equaliser in the 1-1 draw with Tottenham Hotspur.
Mousa Dembele celebrated his Spurs debut by pouncing in the 69th minute with wonderful skill and a fine finish that showed the £15 million ($23.05 million) signing from Fulham at his creative best.
The first half had been controlled by Norwich, with only sharp reflexes from Brad Friedel denying Russell Martin and Snodgrass.
It came as no surprise when Grant Holt set up Snodgrass to level and Spurs' problems grew when substitute Tom Huddlestone was shown a straight red for his tackle on Jonny Howson.
New signing Steven Fletcher struck twice but Sunderland was still forced to settle for a 2-2 draw with Swansea City at the Liberty Stadium.
Fletcher, whose arrival from Wolverhampton Wanderers cost the Black Cats £12 million ($18.44 million), opened his account by tucking home an ill-advised backpass from Ashley Williams.
Wayne Routledge equalised for Swansea but on the stroke of half-time Fletcher stabbed home his second.
Swansea was not finished, however, with midfielder Michu nodding home his fourth goal of the season.
Michu's fellow Spaniard Chico Flores was then shown a straight red card for a dangerous high tackle on Louis Saha.
Peter Crouch nodded home from close range as Stoke City came from behind twice to draw 2-2 with Wigan Athletic at DW Stadium.
Shaun Maloney gave Wigan the lead from the spot after James McCarthy's shot struck Robert Huth's outstretched arm.
Stoke responded in kind through Jon Walters after Maynor Figueroa had handled.
Franco di Santo appeared to have fired the winner after combining well with the creative Arouna Kone, only for Crouch to earn a point for Stoke.
West Bromwich Albion dispatched Everton 2-0, Shane Long opening the scoring after meeting a superb cross from Peter Odemwingie, who had just stepped off the bench.
Gareth McAuley then added the second after poor defending at a corner from Everton to reward the Baggies' dominance at the Hawthorns.
The day's action opened with West Ham United's surprise 3-0 demolition of Fulham at Upton Park.
Loan signing Andy Carroll impressed on his Hammers debut, setting up goals for Kevin Nolan and Matt Taylor with Winston Reid's header contributing to the rout.
Carroll eventually limped off with a hamstring injury which later prompted his withdrawal from England's squad for its opening 2014 FIFA World Cup qualifiers against Moldova and Ukraine.