A solid defensive performance marshalled by the superb Andrew Davies ensured a Rasiak strike just before the half hour mark was enough to clinch victory.
Southampton's generosity of spirit extended to trying to gift Scunthorpe a lead - twice - in the opening minute (and from a Saints' kick off too), as Idiakez started as he went on, by seeming to believe that he had a right to expect several seconds more on the ball than a very physical away team were willing to grant him.
This gave the visitors a reasonable chance to opening the scoring within ten seconds. Saints first chance came on 3 minutes when a sweet ball from Rasiak played Idiakez through behind the defence, but the Spaniard's effort was as high, wide and unhandsome as his dismal penalty kick at Pride Park last May.
Saints' first half threat came principally down the left flank, with Drew Surman in impressive form on the few occasions that he was played into the game by his team mates.
Vignal also started to get involved in the action, showing a good ability to get forward in the few minutes leading up to what was beginning to feel like an imminent Southampton breakthrough, especially given Scunthorpe's profligacy in squandering the chances offered to them by a hapless Jason Euell playing the holding role in the absence of the much-missed Safri and by an out-of-sorts Wayne Thomas.
On several occasions the Davi(e)ses provided a much needed last line of defence. Andrew showing strength, speed and awareness and Kelvin having an almost flawless game in the Number 1 shirt.
Halfway through the first period, Bradley Wright-Phillips found Surman in well-worked space on the left flank and after pushing forward by a few paces, his confident cross was crashed in from the fast-arriving Rasiak from a few yards out.
To maintain their first half lead, Kelvin Davies needed to show good reactions to tip over in the 35th minute - following a rudimenatry error from Thomas - and mere seconds later Andrew Davies was forced to concede a corner as poor communication between the virtually untried pairing of Surman and Vignal let Scunthorpe in down the right wing.
On the stroke of half-time, Idiakez's over-ambition was displayed by attempting to score direct from a free kick from nearly 30 yards out. He did at least hit the target.
Saints came out after the interval determined to get the clinching second goal, but ended it looking like they were expecting to drop points - yet again - in the last stages of the game.
The initial midfield four of Surman, Euell, Idiakez and Hamill had worked acceptably, but Saints' superiority was undermined by a reshuffle following Idiakez's replacement by Viafara in the 52nd minute.
Rather than deploying the Columbian in the holding role and freeing up Euell to act behind the strikers, Hamill was switched to the left-wing (further encouraging his obsessive tendency to tuck inside), Surman joined Euell in the middle (where he was far less effective than he had been in the first half) and a barely match fit Viafara was charged with working the right-side.
The home crowd and players started to lose patience with referee Paul Taylor after the hour mark. A reasonable penalty shout from an apparent Scunthorpe handball had already been turned down. A blistering run from Hammill, in which he covered 50 yards before being brought down in the box and managing to square for Wright-Phillips to put the ball in the net was ruled out for offside.
Seconds later, to exacerbate the Saints' fans sense of injustice and foreboding, the visitors came within inches of an equaliser as Scunthorpe clipped the post from a tidy effort 18 yards out.
By the time Bradley Wright-Phillips was claiming he'd been pulled back in the penalty area in the 67th minute, it was plain that - short of the Scunthorpe defence getting out submachine guns and literally shooting down a Southampton player - the referee was not going to give anything to the home team.
Stern John replaced Rasiak on 65 minutes, but his supposed better ability to hold up the ball did not lead to any more incisive Southampton forays into Scunthorpe's half. And he would have been grateful when his first simple chance (which he fluffed pathetically) would anyway have been ruled out for offside.
With twenty minutes to go, Southampton defended deeper and deeper and seemed content to try and hit Scunthorpe on the counter attack, although these rarely threatened as long balls punted up to John and Wright-Phillips were swiftly fired back towards the Saints's box.
Andrew Davies went down on 72 minutes - apparently with cramp. Had he not made a swift recovery, it seemed likely that the away team would eventually have found a way through the Saints' backline.
With ten minutes to go, Burley threw on McGoldrick for Wright-Phillips. The latter had run himself ragged and shown some nice touches, but still looked unlikely to score. The former showed why he remains a fringe player at this level, with poor positioning, limited understanding with Stern John and an inability to involve himself in the game.
The last few minutes were both tense and violent, with Scunthrpe winning a string of free kicks deep into Southampton territory. One of the biggest cheers came as the referee collapsed to the ground in the midst of a melee.
Following a booking to Viafara, all-out war nearly erupted in stoppage time as Scunthorpe's Matthew Sparrow - who had been needling through out the match - clattered Hammill on the right touchline. To give the referee and linesman some credit, they were able to prevent punches flying and remarkably all 22 players remained on the pitch. The fracas helped Saints as the few minutes of injury time were broken up.
A just-about deserved home win from a team who don't yet look like emulating last season's play-off finish. As for Scunthorpe, this was their first game at Soutahmpton for over 40 years and it seems very unlikely they'll be back here next season. St. Mary's won't be miss them.
So, three points but not much else to cheer about.