The Gunners missed several good chances before they took the lead on the stroke of half-time through an own goal from Latics skipper Antolin Alcaraz.
Wigan lost Victor Moses to a suspected dislocated shoulder and Nicklas Bendtner's close-range effort on 67 minutes kept Arsene Wenger's men on the road to Wembley.
Earlier, Bendtner - recalled to the starting XI alongside Robin van Persie and Theo Walcott - missed a great chance to earn an early lead when he failed to connect with a free header at the far post from van Persie's deep free-kick.
Wigan tried to knock the ball around crisply as Moses darted down the left and cut back inside to the Arsenal penalty area before drilling a low shot into the side netting.
Emmanuel Eboue's careless backpass from the halfway line allowed Mauro Boselli to scamper clear, but fortunately for the Arsenal defender the Argentina forward was pushed wide and eventually the attack broke down.
Carlo Vela's angled drive was deflected out for a corner which Laurent Koscielny flicked over as Arsenal upped the tempo.
The Mexican was put through again on 26 minutes, this time by van Persie's clever backheel, but as the keeper committed himself, Vela's chip curled just wide of the empty net.
Wigan defender Steve Gohouri showed great composure to chest the ball back to his keeper after it was lofted through the six-yard box.
However, when Maynor Figueroa bodychecked Walcott, referee Martin Atkinson immediately reached for his back pocket.
There was then a brief stoppage as Moses received treatment from an awkward fall in the build-up to Arsenal's counter-attack, landing on his wrist.
The England youth international was carried off on a stretcher, replaced by Charles N'Zogbia.
Arsenal appealed for handball against Figueroa as van Persie looked to collect a chip into the Wigan box, but neither the referee nor his assistant were interested, which replays suggested they should have been.
Arsenal went ahead on 42 minutes through an own goal.
Walcott's corner caused all sorts of problems in the Wigan six-yard box, with Alcaraz - just back from suspension - flicking the ball into the net under pressure from Bendtner.
There were some anxious moments for Arsenal at the start of the second half when van Persie needed treatment after being sandwiched between two Wigan defenders as he tried to connect with Vela's cross into the six-yard box.
Walcott weaved down the right and chipped the ball back for Bendtner, but the Denmark striker headed wide.
Wigan continued to come forward and caused some concern around the Arsenal penalty box.
As the hour mark passed, the temperature continued to plummet with snow swirling around inside the Emirates Stadium basin.
Arsenal looked to have secured safe passage to the semi-finals when Vela was put clear down the left, and his low centre was bundled in by Bendtner from two yards after 67 minutes.
Walcott got away again down the right, beating the advancing keeper and pushing the ball out to Vela, but the angle was too tight as Ali Al Habsi recovered to save on the line.
With the tie now safe, Arsenal took off van Persie and Jack Wilshere, who were replaced by Craig Eastmond and Samir Nasri.
Walcott almost made it three when he cut in from the left and curled a low effort just wide of the far post.
It was all too much excitement for one young fan, who sprinted down the touchline to shake hands with Wenger before being escorted away by stewards.
In stoppage time, Nasri broke into the box and rounded the keeper, but his shot was cleared off the line by James McArthur.