The Frenchman's team showed their resilience in the face of a Burnley fightback in their first game since Aaron Ramsey's terrible injury, with Theo Walcott securing victory with a brilliant goal.
Arsenal's win increases the pressure on Chelsea and Manchester United, who went two points clear at the top with a 1-0 win at Wolves and, with the least demanding run-in, the Gunners could even be favourites.
In with a shout: Andrey Arshavin and Theo Walcott celebrate as Arsenal ease to victory at the Emirates
Wenger's players all came out wearing Ramsey's No 16 to honour their team-mate, who is recovering from a badly broken leg.
The Arsenal manager will be desperate not to lose his captain CescFabregas, too, after he damaged a hamstring following his 17th goal ofthe season.
Wenger accepts that he has not had a deep enough squad in recentseasons but he believes his young side now have the necessaryexperience and resilience to claim a double.
Message of support: The Arsenal players wore 'Get well soon Aaron' t-shirts in honour of the injured Ramsey
'I think we can,' he said. 'But it depends whether we keep our players and avoid more injuries.'
Next is the Champions League on Tuesday, when Arsenal have to overcome a 2-1 deficit against Porto to reach the quarter-finals.
'Two months ago I would have said that our best chance is in theChampions League but now I would say that it's the Premier League,'said Wenger.
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