The on-loan Troyes marksman struck twice either side of a Gary Breen own goal in a frantic 11-minute first-half spell before completing a top class hat-trick seven minutes from time.
Leon Best grabbed the fourth in the 55th minute before Andrew Surman added a fifth as Southampton ran riot to end a dismal run that had seen them collect just four points from their previous eight games.
Wolves only had themselves to blame for their heaviest defeat since losing 6-0 to Liverpool in 1968 as they failed to make the most of their early domination and were then defensively poor when Southampton cut loose.
Their misery was summed up in first-half injury time when Michael Kightly missed from the spot - the third penalty that Wolves have been awarded this season and the third they have missed.
All hopes of a comeback were then extinguished ten minutes into the second half when Best rammed home his 11th goal of the season after converting a Nathan Dyer cross at the second attempt following a save by Matt Murray.
Unmarked Surman then curled home the fifth in the 79th minute before Saganowski helped himself to the match ball - taking his tally to seven in ten games for the Saints in the process.
He latched on to a misplaced clearance from Murray before burying the ball into the back of the net from the edge of the area.
Having put together an eight-game unbeaten run, Wolves have now lost two of their last three games and picked up just one point from nine.
Southampton had barely been seen as an attacking force before Surman whipped in a 25th minute right-wing cross that Saganowski powerfully headed home at the far post despite the best efforts of Murray.
Wolves were still reeling from that setback when Southampton were gifted a second.
Rudi Skacel motored down the left flank and fired in a low cross that Murray got a hand to only to see Breen inadvertently turn the ball into his own net.
Wolves briefly threatened to reduce the arrears in the 29th minute when Andy Keogh was denied by a smart save from Bartosz Bialkowski only for Saganowksi to then put the game out of their reach.
Murray was caught in no man's land off his line when Saganowski turned just inside the area and chipped over the head of the former England Under-21 international.
Wolves, who saw Keogh hit the post with a close range header, then tossed away a chance to grab a lifeline on the stroke of half-time when Chris Makin was adjudged to have handled a flick-on from Kightly.
Kightly stepped forward to take the penalty himself only to see his weak spot-kick comfortably saved by Bialkowski.