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...
1. Cheltenham reject second bid for captain
Cheltenham have rejected a second bid for captain Ben Tozer from Wrexham. The National League club had reportedly doubled their first bid to £120,000. (Gloucestershire Live) Photo: Dan Istitene
2. Wolves set to swoop for Cardiff City striker
Wolves are reportedly preparing a late move for Cardiff City striker Kieffer Moore. Bruno Lage’s side are ready to offer £7 million for the 29-year-old. (Football Insider) Photo: Shaun Botterill
3. Barnsley offer $1m to sign New Zealand international
Barnsley have reportedly offered close to $1 million to sign midfielder Joe Bell from Norwegian side Viking FK. Bell was a key figure in the OlyWhites squad that reached the quarter-finals at the Tokyo Olympics last month. (Stuff.nz) Photo: Catherine Ivill
4. Sheffield Wednesday plotting move for former Boro winger
Sheffield Wednesday are reportedly looking at signing Nathaniel Mendez-Laing following the departure of Andre Green. The winger was released by Middlesbrough at the end of last season. (Football League World) Photo: Dan Istitene