The French striker saw red in the 53rd minute for reacting furiously when Nedum Onouha shoved him over and he almost crashed into keeper Rob Green.

The dismissal, which came after he leapt up and confronted Onouha, could have proved costly.

But the Gunners held on to send Rangers to their ninth straight away defeat in the Premier League.

The victory was Wenger's 400th in the Premier League and his 600th overall for the club.

Goals from man-of-the-match Alexis Sanchez and Tomas Rosicky earned it, although the north Londoners looked shaky in the last few minutes after Charlie Austin hit back with a 79th minute penalty.

They also survived strong claims for a second QPR spot-kick at the death with Kieran Gibbs looked to have fouled Bobby Zamora in front of goal.

STAR: Alexis Sanchez was Arsenal's stand out player once again [GETTY]

But the rash actions of striker Giroud, who will be banned for three matches, was the major talking point of the match.

"It was a deserved red card," said Wenger. "He touched him and should not have done it.

"He has apologised and I know him well enough to think he will not do it again. He told me he was pushed in the back and projected again the keeper.

"Maybe it was the injury (broken leg) still plays a part on his mind and he was scared to be injured again.

"It is unusual for him. Honestly, he is usually the type of guy who is in control of his responses and calm."

Arsenal looked to have the perfect start when Armand Traore lunged in on Sanchez in the eighth minute and conceded a penalty.

But Sanchez - who pushed away No 1 penalty-taker Santi Cazorla - fluffed from the spot, sending his low kick to Green's left but not in the corner.

GOAL: Rosicky scored what proved to be the winner [GETTY]

The keeper, who had been advised to dive left by his team-mate Eduardo Vargas - who, like Sanchez, is from Chile - diis as he was told and saved.

But Sanchez made amends for in the 38th minute, heading home Gibbs' cross after a sweeping move.

QPR boss Harry Redknapp called the marking for the goal atrocious, with Traore letting Sanchez drift free in front of goal.

Giroud's dismissal should have changed the balance of the match, but it did not. Sanchez simply charged at Rangers from the half-way line in the 65th minute, with Niko Kranjcar never looking like stopping him.

He then slid the ball across for Rosicky, making his first Premier League start since May, to sidefoot low past Green.

Rangers did respond when Austin scored from the spot, after Mathieu Debuchy caught Junior Hoilett in the box.

RED: Giroud head-butts Onouha and is sent off [GETTY]

And just like at Liverpool six days ago, the Gunners, at 2-1 up, looked "nervous", admitted Wenger.

They could have conceded to draw 2-2 again when Gibbs caught Zamora, but ref Martin Atkinson waved play-on. "It was a blatant penalty," said Redknapp.

"I don't know why he didn't give it, maybe it was because he had already given two. But we weren't positive at 1-0 against ten men and for them to score was the worst thing possible."

ARSENAL (4-2-3-1): Arsenal: Szczesny; Debuchy, Mertesacker, Monreal, Gibbs; Rosicky (Chambers 83), Flamini; Cazorla, Sanchez, Giroud;

Welbeck (Coquelin 88). Subs: Podolski, Ospina, Walcott, Campbell, Bellerin.

QPR (3-5-2): Green; Onuoha, Ferdinand, Caulker; Isla, Mutch (Zamora 71), Henry (Fer 62), Kranjcar, Traore (Hoilett 62); Vargas, Austin.

Subs: Hill, Phillips, Wright-Phillips, McCarthy.

Referee: Martin Atkinson .