Gunners boss Arsene Wenger gave Robin van Persie his first start since returning from injury and recalled striker Bendtner to the frontline.
Latics manager Roberto Martinez dropped winger Charles N’Zogbia to the bench, and started with Victor Moses supporting Mauro Boselli in attack.
As expected, the home side settled quickest and could have been in front within two minutes, but Bendtner could only direct the ball past the right hand post from a Van Persie free-kick.
However Wigan soon settled and although they strung together some nice passes, Moses’ low shot that hit the side netting was the only effort of note.
A bumper crowd had descended upon the Emirates despite the ‘big freeze’ and as the half progressed, the Gunners didn’t give them much to cheer, often being surround by two or three players when on the attack, although defender Laurent Koscielny had a half chance to open the scoring, but headed over from a Theo Walcott corner.
However, the crowd should have been lifted from their seats on 25 minutes when Mexican striker Carlos Vela found himself clean through on goal and managed to chip the ball over the on rushing Al-Habsi, only to see the ball trickle just wide of the left post.
But despite Vela’s bad luck, and a penalty appeal that had been turned down by the referee when the ball appeared to strike the hand of Maynor Figeuroa, Arsenal went in front five minutes before half time.
Walcott drifted a corner in from the left and although Bendtner rose highest, the ball hit Wigan defender Alcaraz and landed in the net.
However the Latics defender almost immediately made up for his own goal, but his header from a Ben Watson corner was easily saved by Wojciech Szczesny as the home side went into the break a goal ahead.
A blizzard greeted the players as the second half began, but it was the home side who again seized control of the game, as their passing and creativity caused problems for the Wigan defence.
The Latics were not buried beneath the snow though and still threatened going forward, with substitute Charles N’Zogbia, who replaced the injured Moses in the first half, looking the most lively, but the final ball was not good enough to trouble the Gunners defence.
And Arsenal made the visitors pay as they doubled the lead just after the hour mark. Vela found space on the left and his low cross was turned in by Bendtner who scored his third goal of the season to all but seal a place in the semi-finals of the League Cup.
The shackles seemed to loosen thereafter for the Gunners as they continued to press and tried to put the result beyond doubt, with Vela and Walcott three times going close for the home side.
There was even time for Vela to add a third for the Gunners towards the end of the game, but Alcaraz cleared the ball off the line for Wigan as Arsenal reached the semi-finals, taking step closer to Wembley.