Ireland started the game well, with Glenn Whelan coming close to an opening goal when he dragged his shot wide from the edge of the box.
Robbie Keane gave his side the lead in the 22nd minute when he took advantage of some poor defending to power the ball in from close range after striking the post with his first effort at goal.
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Ireland had an opportunity to regain the lead just before the break but Jonathan Walters failed to hit the target with a dipping volley.
Winger James McClean was close to handing his side the lead for the second time just after the interval but Andreas Isaksson reacted well to push a low shot away from goal.
Sweden scored the vital goal in the 57th minute when Zlatan Ibrahimovic released Anders Svensson, who made no mistake with a drilled effort past Forde in the Ireland goal.
The home side had a great opportunity to pull a goal back as the game entered its final stages but Shane Long chose to shoot instead of pick out Keane and the West Bromwich Albion forward was left to regret his selfish decision.
Ireland continued to push for an equaliser but the Swedish defence managed to hold firm and secure an impressive away victory.