The visitors fell behind after Villa lost the ball on the edge of their box allowing Keiran Lee to skip past two defenders, teeing up Dion Charles for a simple finish.
But Villa composed themselves with Luiz levelling in unlikely fashion. His inswinging corner looped over the Bolton goalkeeper's head and into the far corner. The sides went into the break all square, but the Premier League side showed their superior ability in the second half.
Ings sent them into the lead from the spot on the hour mark, despite being marginally offside in the buildup to the penalty, before Digne tucked home a third five minutes later. Bailey rounded off the scoring with a direct run and superb finish in the 85th minute.
Elsewhere, it was a poor night for Fulham, who were unceremonially dumped out of the League Cup at the hands of League Two Crawley.
Tom Nichols gave them the lead in the 16th minute against a heavily rotated Fulham, before he turned provider, setting up 18-year-old James Balagizi for their second of the night. Fulham only registered one shot on target in the tie as Crawley were full value to progress into the third round.
Other Premier League clubs had better luck. Nottingham Forest, also playing a rotated side, made easy work of Grimsby Town, beating them 3-0, whilst Southampton sauntered past Cambridge United thanks to two goals from Che Adams and a strike from Dom Ballard, his first for the senior side.
There were also wins for Wolves, Crystal Palace, Brentford and Everton against lower league opposition. Leicester City and Bournemouth both needed penalties to get past their lower league opposition, but the top-tier sides prevailed away from home.
Meanwhile, there were other upsets as third tier sides Derby County and MK Dons saw off West Brom and Watford respectively.
See all the results from the 21 second round ties with Flashscore.