Swansea thought they were heading for a sixth straight Championship victory through goals from Jordi Gomez and substitute Gorka Pintado only to be denied by Poland International Saganowski, who has now scored four in his last three games.
It was made all the more important by the fact the home side had to play for over half an hour with ten men following the second-half dismissal of defender Lee Molyneux for a second bookable offence.
Saints started brightly and nearly forced an opener on 12 minutes when Andrew Surman's corner caused chaos among the defence and Chris Perry's attempted effort from six yards rebounded off three Swansea players before drifting wide.
Four minutes later, Mark Wotte's side had their noses in front but mainly thanks to the ineptitude of Swansea captain Gary Monk.
Monk, a former Southampton trainee, dallied in possession just outside his penalty area allowing Saganowski to steal the ball and be given a clean run at Dorus de Vries.
The Pole though wanted to take the chance with his right foot allowing two Swansea defenders to retreat but he skilfully managed to pick out the bottom corner.
In-form Swansea were rattled and Southampton nearly claimed a second moments later when Saganowski played David McGoldrick through but the young striker mis-controlled and failed to get enough purchase on his shot.
Just after the half hour mark and against the run of play the Swans levelled through the brute force of Jason Scotland, who held off two defenders before freeing Gomez.
The Spanish midfielder took one touch to set himself and then unleashed a fine right-footed drive into the bottom right-hand corner past Kelvin Davis.
With scores level, Southampton defender Molyneux then needlessly chopped down Gomez on the touch-ine to earn a second yellow and leave his team-mates with a mountain to climb.
It got even steeper as Swansea manager Roberto Martinez's decision to bring on Gorka Pintado paid dividends within three minutes as Alan Tate's long-range strike was fumbled by Davis and the Spaniard tapped into an empty net.
Spirited Saints though were not to be outdone and Surman's fine ball over the top caught the Swans defence cold and Saganowski looked up to check de Vries' position before delicately chipping in from the edge of the penalty area.