City had been looking to reclaim second place in the Premier League on Sunday but hopes of a fifth successive win were all but dashed with the early sending off of Dedryck Boyata at Eastlands.
Nasri put the Gunners ahead 20 minutes into a fiery contest and although Joe Hart kept City in contention with a penalty save from Cesc Fabregas, Song and Bendtner finished them off.
Victory lifted Arsenal back into the top four, above City on goal difference, and contradicted recent criticism of the Londoners' record against their perceived title rivals.
The momentum all appeared to be with City prior to the match, which was preceded by a memorial service and minute's applause for their late manager Malcolm Allison.
Carlos Tevez was back to lead the City line while Emmanuel Adebayor, despite a midweek hat-trick, was left on the bench against his former club.
And the hosts appeared in a rush to impress as Boyata, starting ahead of Joleon Lescott, released Tevez with a superb ball down the right after one minute.
Tevez raced beyond the defence and into the area but David Silva failed to make firm contact with his ball into the middle and Lukasz Fabianski saved his scuffed shot.
Tevez then set Micah Richards free down the right but this time Bacary Sagna slid in to deal with the cross.
Yet no sooner had City started to look dominant than Boyata, as the last man, was sent off for bringing down Marouane Chamakh as he raced onto a Fabregas ball.
Mark Clattenburg took time to consider his verdict but showed a straight red card.
After that it became clear Clattenburg was in for a tough afternoon as the tackles started to fly in.
He booked Denilson for a late challenge on Tevez but showed restraint after Nigel de Jong felled Fabregas.
Gareth Barry was shown a yellow card for fouling the Spaniard but Song escaped such punishment for a bad tackle on Silva.
In terms of chances, City had the next when Tevez mishit a shot at Fabianski but Johan Djourou then headed over from a Sagna cross.
The opening goal came after 20 minutes as Nasri played a one-two with Andrey Arshavin on the edge of the box and clipped the ball over Joe Hart.
Fabregas, still being given close attention by City, was booked himself after tangling with De Jong.
City responded by again attacking down the right as James Milner played Richards through.
Arsenal struggled to get back but were relieved as Richards checked back onto his left foot and screwed his shot wide.
Song and Djourou also went into Clattenburg's notebook before the break after challenges on Silva and Tevez respectively.
The game refused to settle down and Clattenburg was called upon again as Vincent Kompany recklessly lunged in on Fabregas just inside the area.
A penalty was the obvious outcome but Hart kept City in the game with a brilliant save from Fabregas' spot-kick.
Fabregas had another opportunity early in the second half after combining well with Chamakh and Nasri but his first-time shot was weak and easily saved by Hart.
City boss Roberto Mancini decided to make a bold change after 52 minutes, gambling on the determination of Adebayor to impress and removing usual talisman Tevez.
An intricate move saw Milner feed Silva inside the box and the Spaniard's curving right-foot shot was brilliantly tipped wide by Fabianski.
Adebayor had a chance from the resulting corner but Fabianski's presence forced him to direct his header over.
Arshavin then drilled a shot straight at Hart from 20 yards as Arsenal continued to push.
Song finished City off in the 66th minute when he grabbed an opportunistic second for the visitors.
Wayne Bridge had blocked a Fabregas pass intended for Chamakh but the ball ran loose and Song, unchallenged, pounced to smash it into the top corner.
Adebayor raised City fans' spirits when he forced a fine save from Fabianski with a firm header but a flag had already been raised for offside.
There was a stoppage 15 minutes from time when an object appeared to be thrown from the crowd as Arsenal prepared to take a corner.
Substitute Bendtner put the result beyond any doubt five minutes from time when he raced clear and finished from a tight angle.
Fit-again £23million signing Mario Balotelli went close to a late consolation when he forced Fabianksi to tip over.