A first half stunner from Mauro Boselli was enough to see Latics set themselves up with a fourth round tie against Macclesfield Town in what was a professional and hard fought 1-0 victory against AFC Bournemouth at the Goldsands Stadium.
The hosts gave a very credible performance and made Latics defend in numbers but the quality of Boselli's strike was enough in the end.
Roberto Martinez made nine changes from the Premier League draw with Fulham at the weekend and made two changes from the side that played Bournemouth in the FA Cup at the DW Stadium, with Roger Espinoza making his debut in English football and Angelo Henriquez handed his first start.
It was a game that saw momentum and discipline ebb and flow as both sides worked hard to force their presence on the game.
The home side showed their hand early on and their tactic was clearly to get ball after ball into the box but, they didn't bank on having Roman Golobart stood in the middle to clear everything that was sent his way.
After holding off the wide play for 18 minutes, Latics made their mark when the tireless Mauro Boselli worked to close down the defence and capitalised from a mistake which saw the ball teed up for him on the edge of the area.
The Argentinian international took one touch and flashed the ball into the top corner with Bournemouth keeper Shwan Jalal getting a touch but not enough to stop the power in the drive.
Latics began to look more comfortable after the goal but it was always to be a night of hard work with the energy that Bournemouth possessed.
Debutant Espinoza proved a crucial go in Latics team play and his ability to break up moves in the middle and create them for his own team gave flashes of his potential.
Bournemouth's best chance of the first half fell to the goal scorer from the first meeting between the two as Eunan O'Kane rattled the cross bar from range as Mike Pollitt sprawled but was beaten.
Latics lived dangerously towards the end of the first half as crosses were allowed to be made but Golobart and Emmerson Boyce controlled the defence extremely well and proved to be rock solid.
The second half was again a battle to keep out the Bournemouth deliveries but, Latics were the team to have the ball in the net again but to Golobart's dismay as he powered a header home, the corner from Espinoza to set him up had swung out of play and back in.
Latics made themselves dangerous on the counter attack on a number of occasions, with the best chance falling to Mauro Boselli from a ball across the box as he nodded the ball low but saw Jalal dive down to push the ball away and then block the follow up by Henriquez.
Another late Latics chance could have sealed the win when Espinoza barged his way into the box and played a low cross to the back post for substitute Nouha Dicko, only for the French winger to side foot wide past a gaping goal.
Bournemouth upped the pressure as the game headed to 90 minutes and blocks from Golobart, Boyce and Figueroa constantly denied them.
Ali Al Habsi (who came on for Pollitt at half time after he suffered a thigh injury) was made to be on guard as Bournemouth lambasted Latics' defence in the four minutes of stoppage time.
Marc Pugh looped a shot onto the cross bar from range to send another warning sign and then with just seconds to go Matt Tubbs' free kick was curling into the top corner only for Al Habsi to leap off his line and tip the ball over.
With a full four minutes of added time played, Jon Moss finally blew the whistle to send Latics through to the fourth round at the expense of a Bournemouth side that gave it their all.