Svensson's second-half goal capped off a momentous night for the midfielder, who took his place in the starting line-up to equal Thomas Ravelli’s appearance record for Sweden.
The hosts took the lead midway through the first half through Robbie Keane, before Johan Elmander levelled with a powerful header.
Things got better for the Swedes in the second half when Svensson slotted home with a cool finish.
The result gives Sweden the upper hand in the race for a play-off spot in Group C and is a blow to Ireland's bid to reach Brazil next year.
Richard Dunne returned to the Ireland starting line-up to make his first competitive international appearance since Euro 2012, while goalkeeper David Forde and Marc Wilson both shook off injuries to start.
James McClean replaced injured winger Aiden McGeady and Shane Long returned from suspension.
Sweden were without Rasmus Elm, who missed out through injury, and suspended defender Andreas Granqvist, while Elmander partnered Zlatan Ibrahimovic up front.
Ireland came into the fixture having not lost at home to Sweden since 1949. And their fans were nearly given something to celebrate within the first two minutes, when Long found space in the box to chest down the ball before unleashing a stinging half volley that was well blocked by Martin Olsson.
It began what was a good opening spell for the home side, with Glenn Whelan carving out several opportunities just before the 10-minute mark as Sweden looked a little nervous.
The visitors struggled to find their rhythm during the opening exchanges, but should have taken the lead after 17 minutes when a flashed corner found Ibrahimovic at the far post, but the Paris Saint-Germain striker could only find the side-netting.
Ireland were undeterred and continued to venture forward, and nearly took the lead after 21 minutes when McClean's cross glanced the crossbar.
Moments later, though, Ireland were ahead when Keane recovered his footing after being brought down by Andreas Isaksson to lash home from close range.
Sweden came back strongly and should have levelled on the half-hour mark when Sebastian Larsson found himself unmarked at the far post, only to direct his header over the bar.
But the visitors did restore parity just a minute later after a whipped cross from Mikael Lustig found Elmander, who powered a header past Forde.
Ireland started the second half with the same level of momentum and carved out an early opportunity within the first six minutes when McClean was allowed to cut inside before sending a swerving effort straight at Isaksson.
But Giovanni Trapattoni's side were dealt a massive blow two minutes later, when Ibrahimovic played in Svensson, who slotted home with a neat finish.
The goal left Ireland stunned, with Sweden gradually taking a greater foothold in the middle of the field, much to the frustration of Trapattoni, who threw on Norwich midfielder Anthony Pilkington for his debut in an attempt to unlock the Swedish defence.
And he nearly managed to earn the hosts a valuable point, finding Long in the centre of the penalty area, who could only direct a tame header straight at Isaksson.
