It was a fourth consecutive victory for Arsene Wenger's side and continued Villa's poor run on their home ground, where they have failed to win in their last five matches and only twice in the league all season.
Christian Benteke's first goal in 13 matches prompted a late burst of Villa pressure, but it was too late to rescue a draw.
Arsenal are now one point clear of second placed Manchester City, with Chelsea a further point behind the leaders, as the title race hots up.
<img src="http://images.mid-day.com/2014/jan/arsenal.jpg" alt="Arsenal vs Aston Villa" width="500" height="374" />
Villa opted to play five at the back in an attempt to keep Arsenal quiet after Paul Lambert's low on confidence side lost 2-1 at home to League One team Sheffield United in their last game.
But France striker Giroud made his return for Arsenal following injury and illness and came close to heading Arsenal into an early lead.
Villa could have taken the lead when Benteke capitalised on a mistake by Wilshere and fed Fabian Delph, who fired just wide from 20 yards.
Lambert's side were hit by a worrying injury to defender Nathan Baker who took the full force of a Serge Gnabry free kick in the face.
The centre half was taken off on a stretcher with an oxygen mask and did not appear to move after being down on the pitch for treatment for six minutes.
Lambert brought on Leandro Bacuna for the stricken Baker and it was later confirmed that the young defender had suffered mild concussion.
The change meant Villa were forced back to a 4-4-2 formation but initially it did them no harm as they went close to taking the lead as Karim El Ahmadi fired over after a promising ball from Delph.
However Arsenal had plenty of possession and they went ahead in the 34th minute.
Mesut Ozil found Nacho Monreal down the left and he crossed for England midfielder Wilshere, who coolly beat Brad Guzan for his fifth goal of the season.
The Gunners scored a second just a minute later after Wilshere capitalised on a Delph error and passed to Giroud, who clinically fired in his 12th goal of the campaign.
Villa had a lively start to the second half with Bacuna shooting left footed at Wojciech Szczesny from Matt Lowton's pass.
Benteke, who put in a much improved performance, had claims for a penalty waved away by referee Neil Swarbrick after tangling with Laurent Koscielny.
Chances came at both ends as Santi Cazorla's left footed volley from the edge of the area was well handled by Guzan before Szczesny saved well from Ashley Westwood in a similar position at the other end.
Arsenal continued to come at Villa with Giroud firing just wide after substitute Kieran Gibbs had crossed from the touchline.
But it was Villa who set up an exciting finale as Benteke at last grabbed his first goal since September, heading home from Lowton's 76th-minute cross after Arsenal had carelessly surrendered possession.
Villa came close to a dramatic equaliser when Delph's drive from the edge of the area was kept out by Szczesny.
Arsenal's nerves were jangling when Tomas Rosicky, a substitute himself, was forced off with an injury to his nose, but they did enough to see the game out.

Arsenal returned to the top of the points with a 2-1 victory at Aston Villa courtesy of two goals within 60 seconds from Wilshere and Giroud

Arsenal beat Aston Villa to go atop the EPL table

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Arsenal beat Aston Villa to go atop the EPL table

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