Ivan Klasnic's fourth goal of the season was enough to edge out Wigan at the DW Stadium and earn Wanderers a last-16 FA Cup tie against Fulham.
The Croatian striker hammered home a 66th minute winner as the Whites extended their unbeaten run against the Latics to seven matches.
Bolton were good value for their win and only another inspired performance from veteran Wigan goalkeeper Mike Pollitt stopped the margin of the victory being more emphatic.
The only disappointment to come out of the trip to the DW Stadium was a serious looking injury to Sam Ricketts, who was stretchered from the field at the start of the second half.
As expected, Owen Coyle made several changes to his starting line-up with Adam Bogdan, Fabrice Muamba, Martin Petrov and Ivan Klasnic all earning recalls to the first eleven.
Another man back in the team was Chung-Yong Lee and he fired just wide of the target from outside the area with only two minutes on the clock.
Indeed, it was a lightning quick start from Bolton who had a goal disallowed for offside in their next attack when Elmander converted from the rebound after Mike Pollitt had parried Petrov's fierce left-footed effort.
It was to prove the start of a lively first 45 minutes in which Wanderers somehow failed to break the deadlock despite well and truly bossing the game.
That was mainly down to the form of Mike Pollitt, who made a hat-trick of important saves to keep the Whites at bay.
The Bolton-born keeper denied Elmander from a tight angle, stood up strong to block a Klasnic effort after the Croatian had sprung the offside trap and also acrobatically tipped a Petrov half-volley over the bar when at full stretch.
The one time that the Whites did beat Pollitt they were thwarted by the woodwork as, just moments before the half-time whistle was blown, Elmander hit a low free-kick from 25-yards that struck the inside of the post before rolling out to safety.
At the other end of the pitch, it was a strong first-half showing from the Wanderers defence.
David Wheater brought a cheer from the 3,000 strong travelling contingent with a thunderous, no-nonsense challenge on Wigan's midfield enforcer Hendry Thomas, while Bogdan twice did well to hold on to efforts from Jordi Gomez , the latter being a 25-yard free-kick on 35 minutes.
The start of the second half followed a similar pattern to the first with Bolton coming out after the break and dictating the play.
But Wanderers were dealt a big blow just ten minutes after the restart when Sam Ricketts innocuously slipped inside his own area and needed to be carried from the field on a stretcher.
The Welshman's injury meant a tactical reshuffle from Owen Coyle with Paul Robinson shifting over to right-back and Marcos Alonso slotting in on the left side of defence.
The change in personnel didn't hamper the Whites as they continued their search of the opening goal, which duly arrived from the left boot of Klasnic on 66 minutes.
Just moments after Elmander had seen a second goal of the game disallowed for offside, Klasnic seized on a perfectly weighted slide-rule pass from Mark Davies before hammering across Pollitt and into the back of the net, sending the away fans wild.
But those chants and cheers were almost silenced when Gomez struck the crossbar in Wigan's first attack since going a goal behind. Former Chelsea man Franco Di Santo cut the ball back for the Spaniard, who side-footed against the upright from 12 yards out.
Naturally, Wigan upped the pace in the last 20 minutes as they faced elimination from the FA Cup. Di Santo glanced a header wide of the far post while substitute Victor Moses and centre-half Steven Caldwell saw shots also directed off target.
But Wanderers, who had looked dominant in defence all evening, held firm to record a third clean sheet in their last four games and book their trip to the capital on Sunday afternoon.
Wigan: Pollitt, Gary Caldwell, Thomas, Di Santo, Steven Caldwell, Gomez, McArthur, Diame, Stam, Lopez, McManaman (Moses 43) (Subs not used: Kirkland, McCarthy, Watson, Golobart, Mustoe, Redmond)
Wanderers: Bogdan, Robinson, Cahill, Wheater, Ricketts (Alonso 56), Petrov, Muamba (Cohen 90), Mark Davies, Chung-Yong, Klasnic (Kevin Davies 84), Elmander (Subs not used: Lainton, Taylor, Rodrigo, Blake)