Last updated on .From the section Premier League

Olivier Giroud was sent off at the beginning of the second half

Win moves Arsenal above Spurs to sixth

Victory is Arsene Wenger's 400th in the Premier League

Giroud sent off for headbutt on Onuoha

QPR have now lost all nine away league matches

Arsenal remain within touching distance of the Premier League's top four after victory over QPR - but only after being reduced to 10 men and conceding a second-half penalty.

Alexis Sanchez missed a spot kick but later headed Arsenal into the lead.

Tomas Rosicky doubled their advantage after Olivier Giroud was sent off for a headbutt on Nedum Onuoha.

Then, in a nervy climax, Mathieu Debuchy felled Junior Hoilett and QPR's Charlie Austin converted from the spot.

That was his 12th league goal of the season and set up a dramatic final 10 minutes, but QPR were unable to breach Arsenal's defence for a second time.

A team which has yet to win a point away from home was just the sort of opponent Arsene Wenger's side needed after a period in which the manager has come under heavy criticism.

But the Frenchman will not thank his compatriot Giroud for his senseless reaction to a Onuoha push, which forced the hosts to play the majority of the second half with 10 men, nor Debuchy for the penalty he conceded, adding needless drama to what should have been a routine win.

Sanchez the key man Alexis Sanchez (10 goals, six assists) has scored or assisted half of Arsenal's 32 Premier League goals this season. Ian Wright (14) is the only player to reach 10 Premier League goals in fewer games for Arsenal than Sanchez (17). Only Cesc Fabregas (12) and Gylfi Sigurdsson (8) have more league assists than Alexis Sanchez's six this season. Alexis Sanchez now has 15 goals in all competitions for Arsenal this season, level with Tottenham's Harry Kane.

The Gunners have nine points fewer than at the same stage last season, when they were level with league leaders Liverpool.

Indeed, a Boxing Day victory was a must if title hopes were not to be completely extinguished before the end of the year.

Even after victory, which was Wenger's 400th in the league, Arsenal remain 15 points behind leaders Chelsea and two points adrift of fourth-place Southampton, with every team in the top four also enjoying wins.

This was an improvement of sorts on last week's display against Liverpool, but Arsenal are unlikely to come up against a team as obliging as QPR were in the first half.

Harry Redknapp men's somehow soaked up wave after wave of attacks until, eventually, they caved in seven minutes before the break.

A lovely move, featuring Danny Welbeck, Santi Cazorla and Kieran Gibbs, was finished off by Sanchez to give his team a deserved lead.

That made up for the Chilean's miss from the penalty spot after he was challenged clumsily by Armand Traore, with the diving Robert Green saving Sanchez's tame effort.

A hint of the defensive frailties which have plagued the Gunners this season was given when Steven Caulker sneaked behind the defence and headed a fraction wide.

But although Giroud gifted the QPR a lifeline, the visitors were unable to test the Arsenal back four before Rosicky scored.

Sanchez was the creator, elegantly weaving his way towards the box before releasing the equally impressive Czech, who swept home on his first league start of the term.

Until Debuchy was penalised for bringing down Hoilett - though replays showed the defender did make contact with the ball - QPR were unable to test Arsenal.

And although Austin, quiet for much of the match, scored to set up a grandstand finish, Arsenal held firm to inflict a ninth away loss on QPR.

Robert Green saved a Premier League penalty for the first time since November 2010

Arsenal have only lost one Premier League match on Boxing Day

Olivier Giroud's 53rd-minute sending off played a part in Arsenal's nervy finish

Charlie Austin has now scored 10 goals in his last nine league games