Despite the Latics seeing Jordan Jones’ penalty saved, Bolton’s Kieran Lee also failed to score.
Goalkeeper Jamie Jones rifled home his spot-kick and a miss by Nathan Delfouneso sent the home side through to the next round.
On the penalty shoot-out win, Wigan boss Leam Richardson said: "It's something we've missed over the last couple of years , that kind of atmosphere...11 and a half thousand on a Tuesday night against a team down the road in a big derby.
"The buzz in the ground was fantastic, I thoroughly enjoyed it.
"The only downside was we weren't lucky enough to be out there with the players and enjoying it from the middle!”
Here is the best of today’s Championship and League One rumours...
On the penalty shoot-out win, Wigan boss Leam Richardson said: "It's something we've missed over the last couple of years , that kind of atmosphere...11 and a half thousand on a Tuesday night against a team down the road in a big derby.