The 37-year-old midfielder fired home from Zlatan Ibrahimovic's slide-rule 57th-minute pass to help the Swedes complete a stirring comeback in front of a packed house.
It had started so well for Ireland when Robbie Keane blasted them ahead with 22 minutes gone, the 60th goal of his senior international career.
Johan Elmander levelled after 33 minutes with a bullet header to pave the way for Svensson to finish the job and arguably, Ireland's hopes of making it to Brazil next summer.
Giovanni Trapattoni's men will head for Austria on Tuesday night knowing nothing short of victory will give them any chance of wrestling back a chance of snatching second place in Group C, and even them they might have to do something special away to runaway leaders Germany to achieve it.
Shane Long, challenged by assistant manager Marco Tardelli during the week to improve his finishing, might have provided the perfect riposte within a minute of the kick-off only for full-back Martin Olsson to make a brave block after defender Richard Dunne had headed down Seamus Coleman's free-kick for the striker.
Glenn Whelan thumped a shot from distance into Swedish keeper Andreas Isaksson's midriff after slicing an earlier effort wide, and Jon Walters drove past the post in an encouraging start by the home side.
Ibrahimovic had in the meantime wasted two free-kicks, sending both into the defensive wall, but Marc Wilson had to redeem himself after allowing a 16th-minute cross to drop over his head to the Paris St Germain frontman by getting in a good block to repel the ensuing shot.
Ireland were almost undone from the resulting corner when Sebastian Larsson's set-piece was helped on to Ibrahimovic beyond the far post, but he could not react quickly enough and stabbed his effort into the side-netting.
But Trapattoni's men forced their way in front with 22 minutes gone, and the identity of the scorer came as little surprise.
James McClean had already served warning by dropping a cross on to Isaksson's bar with the goalkeeper beaten, but the visitors failed to take heed.
Full-back Mikael Lusting's careless header allowed skipper Keane to race in on goal and toe-poke the ball past the advancing keeper, only for it to come back off the foot of the post.
Sweden appeared to have got away with it as Mikael Antonsson and Lustig pounced on the rebound, but between them, they could only serve it up for the Ireland skipper once again and he gleefully lashed it into the roof of the net.
However, the lead lasted just 11 minutes despite a glaring miss by Larsson, who headed wide from Ibrahimovic's cross with the goal at his mercy.
Elmander was far more deadly when he opportunity arrived, getting ahead of 33-year-old Dunne, playing his first competitive game for the Republic for more than a year, to power Lustig's cross home.
The two sides returned after break equally aware of the consequences of both victory and defeat, and it was the Swedes who were first to threaten when Elmander met Olsson's left-wing cross at the near post, but flicked just wide under pressure from Dunne.
McClean forced Isaksson into an uncomfortable 51st-minute save after Long and Walters had combined well on the edge of the penalty area, but it was opposite number David Forde who found himself in the thick of the action as Sweden made their move.
The 33-year-old raced from his line to deny Larsson after he had run on to Ibrahimovic's exquisite through-ball, but was powerless when the striker repeated the dose to set Svensson free, and his finish was assured.
Trapattoni's response was muted - he sent on Simon Cox and then debutant Anthony Pilkington, but to little avail as Sweden saw out time comfortably.