Ivan Klasnic's second half goal was enough to send the Wanderers through to the Fifth Round and their prize is a trip to Craven Cottage this weekend.
Meanwhile, the Latics will be earning a much needed rest ahead of the visit of Manchester United to the DW Stadium.
Here is the reaction of the two managers.
Roberto Martinez
Without playing too well there were some positive performances from the game. I felt that two or three individual displays showed players who are ready to help the team for the remainder of the Barclays Premier League season.
It was a game we wanted to win, but also a game we wanted to take certain lessons from and learn more about where players are up to, and in the case of three players we have good options that will strengthen us from now until May.
Callum McManaman received a nasty cut to his head and needed ten stitches. That was a real shame because he was looking lively and it was a perfect game for him.
We wanted to bring Callum back on and being so close to half-time we were prepared to wait for him to come back out, but his cut was so deep that he wasn't able to play any further role.
Overall there are many good things we can take from the game that will give our league campaign a boost. We gave the ball away quite cheaply and offered them the opportunities in front of Mike (Pollitt) who was excellent tonight.
He used his experience well, was there for the team in a couple of one-on-one situations and helped the team through some tough moments. Jordi worked very hard playing in a difficult position.
He was one of the positives tonight and it's important that we use his quality; he has that final pass and was unlucky to hit the cross-bar because nine out of ten times that would have found the back of the net.
Owen Coyle
I thought we were terrific from start to finish. We created numerous goalscoring opportunities and if the truth be told we could have won by more than the one goal that we scored.
Mike Poillitt has pulled off a number of tremendous saves in the Wigan goal but we kept persevering and ultimately got the goal we deserved.
We know that Ivan Klasnic is the kind of player who is always going to get goals. He could have had three or four tonight but the one he did get he took it wonderfully well. That is the mark of a top class finisher who always poses a threat regardless of who we are playing. He has had a bit of a stop-start season due to injury, but tonight we saw the quality he possesses.
All in all it's a great victory for us and it takes us into the last 16 of the cup and sets us up for a tough away tie against Fulham on Sunday. I felt as a unit we looked strong and the players that came in did wonderfully well.
We have real competition for places. Fabrice has come in and was assured in midfield which meant we did not have to use Stuart. We've managed to pick up three wins in our last four games and it could easily have been four out of four. What now have to keep continuing to do is move in the right direction.
Next game
Next up for the Latics is the visit of Manchester United to the DW Stadium on Saturday 26th February.