The Croatian was handed his first start since rejoining Wanderers in the summer as one of nine changes made by boss Owen Coyle.
And Klasnic, who hit eight goals last term while on loan from Nantes, sank Southampton with an opportunist first-half strike.
Coyle was also indebted to Hungarian youngster Adam Bogdan, who was given his debut in goal and produced a string of fine saves as Bolton, with an eye on Premier League survival and just Kevin Davies and Zat Knight surviving from Saturday's win at West Ham, avoided a shock.
Mind you, such is the standing of this competition, especially the early stages, that Saints also have bigger fish to fry this season and will not shed too many tears at bowing out.
They are favourites for promotion this term, and although currently without a win in League One so far, Alan Pardew's side quickly got amongst their top-flight opponents.
Their striker Rickie Lambert, last season's top scorer in the Football League with 37 goals, looks a player from a bygone age and not just because of Saints' retro kit.
He may be a classic old-fashioned centre-forward but he showed a classy touch to float in a cross which Adam Lallana headed straight at Bogdan.
His strike partner Lee Barnard's angled drive then fizzed narrowly over with just five minutes on the clock.
Bogdan then stepped up to the plate, pulling off saves to deny Lallana, Jason Puncheon and the pick of the bunch from Barnard as the forward raced through.
Bolton finally managed a shot on target in the 28th minute but Kelvin Davies was not unduly troubled by Ricardo Garner's effort.
But within seconds Saints found themselves behind, former Southampton striker Davies knocking down Sam Ricketts' cross for Klasnic to prod home.
Saints momentarily thought they had a chance to equalise when Lallana tumbled in the area but referee Keith Hill booked the you midfielder for a dive.
Coyle brought Klasnic off after the break to give Johan Elmander, Saturday's two-goal hero at Upton Park, a run-out.
The Sweden forward almost made an instant impact with a fierce shot which flew inches over the angle of Davis' post and crossbar.
Saints continued to plug away, though, and continued to find gaps in Bolton's defence with Puncheon firing narrowly wide.
Bogdan almost made a mistake on the hour when he fumbled another Puncheon blast, but the young keeper was up like a shot to leap on the ball before Barnard could pounce.
Half of St Mary's thought Saints had levelled in the 67th minute but Lambert's swerving free-kick had hit the side-netting.
Bogdan was in action again in the 72nd minute when he tipped Danny Butterfield's long-range drive around the post.
As Saints tired Coyle's side nearly added a second with Mark Davies fizzing a shot just over and home keeper Davis clawing away Elmander's acrobatic effort.
But there was still time for Bogdan to deny Saints once more, finger-tipping a stoppage-time effort from sub David Connolly over the top.