The Blues dominated proceedings in front of a 7,344 crowd at Oakwell and claimed a 4-0 aggregate win after also winning 2-0 in the Faroe Islands two weeks ago.
Vedran Corluka and Gelson Fernandes came into the starting line-up after their Euro 2008 commitments, while Elano and Daniel Sturridge looked lively after also coming in.
City had a host of chances and Corluka headed against the crossbar just after the half-hour mark before man-of-the-match Martin Petrov fired against a post in first-half stoppage time.
Petrov finally broke the deadlock 3 minutes after the restart, though, with the Bulgarian winger, who also scored in the 1st leg, sidefooting home from Darius Vassell's low cross.
Mark Hughes' men remained firmly in charge until Vassell raced onto a flick by substitute Ched Evans and went round the keeper before slotting home a deserved goal in the 90th minute.
City: Hart; Corluka, Dunne, Richards, Ball; Elano, Johnson, Fernandes (Hamann 61), Petrov (Etuhu 70); Vassell, Sturridge (Evans 70).
Unused Subs: Schmeichel, Onuoha, Ireland, Bianchi.