Paul Gallagher salvaged some pride late on but the Pole's quick-fire double had already done the damage to sink the Potters for the first time in their last six outings.
Southampton only needed three minutes to create an opening. Claus Lundekvam looked odds on to covert a Rasiak centre before Andy Wilkinson made a last-ditch intervention.
A drab 20 minutes followed with neither side looking in a particularly creative mood until on loan Tottenham striker Rasiak turned the screw.
The striker was on the receiving end of a wild lunge by Marlon Broomes after skipping into the Potters box with some ease and he dusted himself off before promptly slamming home a 27th minute penalty.
Seven minutes later Jermaine Wright whipped in a perfect free-kick and the lofty frontman finished off an outstanding first-half display with a bullet header.
The Britannia faithful were forced to wait 53 minutes to see the home side take a meaningful aim on Kevin Miller's goal.
Substitute winger Peter Sweeney fired off a 20-yard volley which in truth would have benefited from as much attention to accuracy as there was to power.
Gallagher hauled the out-of-sorts home side back in with a shout and staked a late claim for the goal of the season.
He picked out the Southampton top corner with a wicked drive following a neat exchange with Adam Rooney but it was too little too late.