The Poland international, who has been in and out of the Saints starting line-up after a fall-out with manager George Burley, latched onto Andrew Surman's low cross on 25 minutes.
It proved to be the difference as Southampton got their promotion campaign back on track.
For Scunthorpe it merely continued their poor run in the Championship, as they have just one win from their last 17.
It could have been so different for the away side, who went close twice inside the first minute as striker Martin Paterson tested Kelvin Davis from range on ten seconds, before midfielder Ian Morris then missed a fine opportunity 30 seconds later.
Southampton too were not without their chances in a game which saw the sides meet for the first time since 1964.
Rasiak fed the fit-again and restored Inigo Idiakez on goal, only for the Spaniard to shoot embarrassingly over.
Bradey Wright-Phillips then pounced upon a mistake by Shelton Martis to give himself a clear route to goal but skewed wide.
The Southampton striker though partially made up for his wastefulness in front of goal by freeing Surman down the left-hand side for the opener.
The young midfielder could have opted to shoot himself, but instead chose to roll the ball across to the grateful Rasiak, who saw the back of the net bulge for the first time since September 22.
Scunthorpe tried in vain to push for an equaliser before the break and Paul Hayes went close as he capitalised on a Wayne Thomas mis-kick only to see his looping header well tipped over by Davis.
The second-half failed to match the ferocity of the first as Paterson was denied again by Davis from distance on 50 minutes, before Saints had a worthwhile penalty shout turned down after Adam Hammill was clipped by Andy Crosby.
Matthew Sparrow crashed a 25-yard effort against the crossbar and substitute Jonathan Forte forced Davis into an another impressive save, but that was as close as Scunthorpe got to finding an elusive equaliser.