Mauro Boselli scored the only goal of the third-round replay in the 18th minute as he received possession in the Bournemouth half before advancing towards goal and firing home from 20 yards out.
Roberto Martinez stuck to his cup format and made a number of changes despite seeing his side held 1-1 at the DW Stadium in the original tie, with the Latics booking a trip to non-league Macclesfield in the next round.
There was not much to choose between both sides and the hosts certainly showed they were not going to roll over easily and twice saw long-range efforts crack against the crossbar.
Bournemouth's fans would have been buoyed by the way they matched their top-flight opponents until Wigan broke the deadlock after 18 minutes. Cherries midfielder Harry Arter slipped on the ball to gift possession to Boselli, who arrowed a shot into the top corner of Shwan Jalal's goal from 20 yards out.
Callum McManaman came close to a second for the visitors after his close control in the box allowed him to fire a low shot which was well held by Jalal.
Eunan O'Kane, who opened the scoring at Wigan, was inches away from scoring a memorable equalising goal late on in the first half. The former Everton trainee stole the ball in the Wigan half and played a one-two with Wes Thomas before rifling a shot that left Mike Pollitt stranded but thundered against the bar.
A long throw from Charlie Daniels caused a moment of panic within the Wigan box with an hour on the clock but Josh McQuoid could not make good enough contact at the back-post to steer a header past Ali Al Habsi, who had replaced Pollitt at half-time for Wigan.
The visitors broke and an Angelo Henriquez effort forced a corner from which Roman Golobart thought he had doubled their lead - but the effort was ruled out for a foul in the build-up.
Arter, looking to atone for his first-half error, stung the palms of Al Habsi with 68 minutes gone as the Oman goalkeeper could only push his long-range effort behind for a corner. Substitute Wes Fogden then saw a goalbound effort blocked by Golobart before Jalal made a superb save to prevent Boselli netting with a low header.
Bournemouth continued to attack in an attempt to take the tie to extra-time but found the crossbar in the way once more when substitute Mark Pugh's 30-yard effort cannoned back off the woodwork with less than five minutes of normal time remaining.
Nouha Dicko screwed a fantastic chance wide in injury time which would have given the visitors a flattering two-goal margin before a Matt Tubbs free-kick was turned around the post by a fully out-stretched Al Habsi as Bournemouth searched in vain for an equaliser.