After picking up four points from a possible 15, City had been in danger of being dragged back into the relegation quicksand.
There was additional pressure after City had been held at home by bottom club West Brom in their previous fixture.
City, after a nervous opening, produced a vastly improved display and ought to have triumphed by a far wider margin.
In the end they had to settle for first-half goals from Paul Bosvelt and Shaun Wright-Phillips.
But with better finishing they would have inflicted an even heavier defeat on the Saints, where new manager Harry Redknapp has a battle on his hands to retain their Premiership status.
Injury-hit City had Ben Thatcher returning at left-back in place of Stephen Jordan who was hurt against West Brom.
Saints restored striker Kevin Phillips to their line-up, as youngster Dexter Blackstock dropped out.
City looked like a side lacking in confidence in the early stages, but their nerves were settled by a 19th minute goal.
Richard Dunne headed Robbie Fowler's corner back across the face of goal and Bosvelt glanced home a header, only his second goal of the season.
It looked as though City's failing could again be a lack of finishing power as Nicolas Anelka, Shaun Wright-Phillips and Fowler all ought to have added to City's lead.
Fowler was particularly unlucky as he saw his goalbound header beat keeper Antti Niemi, only to be cleared off the line by Danny Higginbotham.
Saints threatened briefly and City keeper David James had to race to the edge of the penalty area to thwart Neil McCann.
City eventually doubled their advantage in the 40th minute with a brilliant solo goal from Wright-Phillips, the youngster picked up the ball in the centre of the field, beat a couple of opponents on a galloping run then thundered home a shot from 30 yards which flew into the net off an upright.
Saints made a double half-time substitution, taking off Brett Ormerod and Matthew Oakley and replacing them with Peter Crouch and Fabrice Fernandes.
Saints were far more of a threat in the second period with Kevin Phillips having a goal ruled out for offside and Crouch being denied what appeared a certain goal by a breathtaking save from James.
Saints were handed an unexpected lifeline in the last minute, when referee Chris Foy controversially ruled that Sylvain Distin had barged Crouch off the ball and Phillips smashed home the resulting penalty.
City never looked like surrendering their lead in the dying seconds and emerged far more comfortable winners than the scoreline suggests.
Man of the Match: Shaun Wright-Phillips – The England winger was at the centre of most of City's best work and lit up the game with a superb solo effort just before half-time.