Klasnic scores the match-winner to set up a game against Fulham.
Bolton beats Wigan in FA Cup replay
The Croatia striker slid home a finish in the 66th minute after latching on to a pass by midfielder Mark Davies to settle a hard-fought northwest derby at DW Stadium.
The Bolton striker Johan Elmander hit the post and had a goal disallowed, while the closest Wigan came to an equaliser was when Jordi Gomez shot just over.
Bolton will travel to Fulham in the fifth round on Saturday.
In the second-tier League Championship, Nottingham Forest missed a chance to go second and move to within four points of leader Queens Park Rangers by losing 1-0 at Scunthorpe.