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The Spaniard headed home from close range six minutes from time, shortly after Stephane Mbia had been given his marching orders for violent conduct.
The Hoops improved after the break and had the ball in the net on 54 minutes, but Junior Hoilett's superb lob was correctly ruled out for offside.
Arsenal soon regained the initiative, Santi Cazorla and Giroud both creating - and spurning - good chances.
QPR were forced to play out the final 10 minutes a man down when Mbia was shown a straight red card for lashing out at Vermaelen.
It took Arsenal just four minutes to make their numerical advantage count, Arteta heading the ball over the line from point-black range after Cesar had done brilliantly to deny Giroud and Aaron Ramsey.
Jamie Mackie missed a golden chance to earn a point for his side in stoppage time, when he fired straight at Vito Mannone from five yards.