Andrew Surman's deflective drive put the home side on their way into the hat for the fifth round before Grzegorz Rasiak made the result absolutely sure by converting his own missed penalty.
It could however have been so different had Bury taken their chances inside the opening five minutes.
Richie Baker struck the base of Kelvin Davis' post with a 25-yard free-kick on two minutes before he was set free moments later for a one-on-one situation only to be denied by the Southampton keeper.
The Championship side, still smarting from the departure of George Burley to take over as Scotland boss, looked disjointed in the opening 20 minutes and struggled to string any genuine passing moves together.
Bradley Wright-Phillips though did go close after strike partner Rasiak had headed a Surman cross into his path but his volley on the turn flew just wide.
Moments before the break, in what was largely a dull and dour first half, Gregory Vignal slammed a long-range free-kick just wide of the post and, as the Saints struggled to break the deadlock, a shock looked increasingly likely.
Indeed as Andy Bishop sped through on 47 minutes the 2,000 or so Bury fans who had made the trip south, thought his low strike may have crept inside the far post only for Davis to make a finger-tip save.
That hope evaporated as Southampton took the lead when Wright-Phillips' run was halted by a string of tackles and, as the ball found its way to the edge of the penalty area, Surman slammed a shot off the feet of Steve Haslam for the ball to creep past Jim Provett.
Bishop was agonisingly close two minutes later to bring the scores level as he headed Nicky Adams' cross against the bar before Rasiak broke Lancashire hearts 12 minutes from time.
Southampton substitute Stern John was bundled over by Ben Futcher and Rasiak stepped up to see his penalty saved. His follow-up was saved again but, in almost comical fashion, he finally stabbed the ball home at the third attempt.