Ten-man Town claimed their second 1-0 win in as many games after a Herculean performance and Charlie Austin's 15th goal of the season clinched an excellent three points at St. Mary's.
The hosts came out of the blocks the quickest, and could have gone ahead but for a sharp early save from Phil Smith to prevent a Rickie Lambert flick looping into the far corner.
And despite a couple of encouraging breaks from Simon Ferry and Jon-Paul McGovern, the Saints were largely dominant for the opening 15 minutes.
However it was Town who should have been in front, when Charlie Austin found himself with a clear shot at goal after good work from Simon Ferry, but the 14 goal front man dragged his left footed effort just wide when he looked certain to score.
The Saints thought they had taken the lead after 26 minutes, when Lee Barnard poked the ball over the line after Lambert's volley had hit the post, but the former Southend man wheeled away only to see the linesman's flag aloft, and Town breathed again.
The game then lost some of its previous momentum, as both sides struggled to get a hold of possession - a pattern which wasn't helped by the lengthy treatment and eventual substitution of Cuthbert, despite his attempts to carry on.
The Saints then proceeded to end the half as they had started it, and Town were hanging on as the three minutes of injury time were played out, with Smith being called upon to make two sharp reaction saves, and Jonathan Douglas covering well to clear a Jason Puncheon shot off the line.
Town were resolute in the first period, but will have been glad to hear the half time whistle after coming under considerable pressure towards the end of the period.
Mark Marshall battles with defender Wayne Thomas
However, the visitors started the second half at a brisk pace and looked threatening from its outset, with both Danny Ward and Simon Ferry breaking forward at every opportunity.
Where it had been Southampton who swept the ball around with confidence in the early stages of the first half, so it was Town who looked the most assured in possession in the second, and they could have gone ahead through Charlie Austin, who stole in at the back post and volleyed Ward's cross on target, but Saints 'keeper Kelvin Davies did well to push it wide.
But minutes later Austin went one better when he was set free by Mark Marshall and calmly rounded the stranded Davies before rolling the ball home into the empty net to give the visitors a deserved lead after a dynamic opening 15 minutes.
The hosts looked shell shocked and struggled to control an increasingly confident Town side, whose strings were being pulled effortlessly by Ferry and Douglas in the centre of midfield.
The home side then upped the pace, bringing on strikers Papa Waigo and David Connolly and moving to a 4-3-3 formation.
It nearly paid dividends as Lambert caused problems again but was denied by the crossbar after unleashing a rasping drive from the edge of the box.
While Town still looked dangerous on the break, Alan Pardew's side began to throw caution to the wind with 10 minutes remaining, and put the Town backline under steadily increasing pressure.
Great work from substitute David Connolly almost produced the equaliser, but the striker's low cross was excellently intercepted by Stephen Darby inside the six-yard box, and Puncheon's follow up was smartly held by Smith.
Phil Smith shouts the instructions ahead of a free-kick
Town then suffered a setback as Simon Ferry was sent off for a second bookable offence after a foul on Adam Lallana, and it really was all hands to the pump form then onwards as the hosts sensed an equaliser.
However Town's rearguard, led by the ever heroic Gordon Greer and the impressive substitute Lecsinel Jean-Francois held out for a hard earned clean sheet, and a massive three points.