Poland international Saganowski struck twice in the first half to take his tally to six in seven games and give Southampton only their second home win of the season and their first home win on a Saturday since April 5 2008.
Andrew Surman fired Southampton ahead on 19 minutes, a convincing left-foot finish after David McGoldrick's twisting run had unsettled a shaky Preston defence.
Saints could have doubled their lead with Jason Euell's looping header from Rudi Skacel's cross, producing a great save from Andy Lonergan.
Meanwhile former Saints defender Andrew Davies, on loan at Preston from Stoke, almost marked an unhappy return to St. Mary's after he looped a defensive header on the top of his own crossbar.
Saganowski gave Southampton a cushion of a second goal on 29 minutes in spectacular fashion.
Adam Lallana laid the ball back to Saganowski, who chested the ball down before dipping a volley over Lonergan from 25 yards.
McGoldrick's volley from a similar distance produced a sharp save from Lonergan, before Saganowski stretched the struggling Saints lead even further on 41 minutes.
Simon Gillett robbed Preston striker Jon Parkin deep inside the Southampton half and fed Saganowski who carried the ball half the length of the pitch against Preston's desperately back-pedalling defence, before tricking his way inside to bury a shot past Lonergan.
Preston's only first-half effort saw Parkin screw a shot wide from 12 yards and Lillywhites boss, Alan Irvine, was so disgusted with Preston's first-half performance, that he made three substitutions at the start of the second half.
He replaced Andrew Davies, Chris Sedgwick and Barry Nicholson with Youl Mawene, Chris Brown and Richard Chaplow.
His side might have trailed even further but for Lonergan, who dived full length to keep out Lallana's near-post header.
Preston huffed and puffed their way back into the game and threw themselves a lifeline on 71 minutes with a goal from their shot on target.
Euell's challenge on Billy Jones saw the ball fall for Ross Wallace, who curled a sweet shot around Kelvin Davis in the Southampton goal.
Preston at last showed some resistance and Parkin was denied at the near post by Davis when he had team-mates waiting and the big striker then nodded a ball down for Sean St Ledger, who tucked the ball past Davis only for Lloyd James to scamper back and hook the ball off the line.