Elmander, who has scored just twice in the Premier League this season, showed quality rarely seen at the Reebok Stadium with a fine strike on the stroke of half-time. Ola Toivonen had earlier had a header ruled out for offside but a youthful Wales side battled hard in the second half and substitute Robert Earnshaw twice went close.
Wales, without the dynamism of Craig Bellamy and the creativity of the injured Aaron Ramsey lacked sparkle early on but their overall efforts offered encouragement for the UEFA EURO 2012 qualifiers next season.
Tottenham's Gareth Bale was particularly impressive after the break and with more players available, John Toshack's side could make a mark in a group that includes England.
Sweden may be going through their own transitional phase under new coach Erik Hamren after failing to qualify for the FIFA World Cup™ for the first time since 1998, but they still boasted plenty of knowhow. Former Aston Villa captain Olof Mellberg was winning his 100th cap while skipper Anders Svensson, once of Southampton, and Birmingham's Sebastian Larsson added substance.
Then there was Elmander, widely regarded as a £10million flop since being signed by former Bolton boss Gary Megson in 2008, showing the class that justified his fee for almost an hour.
Sweden coach Hamren joked of his matchwinner: "He has potential! I was his coach when he was 18 and playing in Swedish division one. It was a really good finish - exactly how I taught him when he was 18."
Yet the match had a low-key feel to it with a crowd of just 8,258. In-form Hull goalkeeper Boaz Myhill was handed the number one jersey but then replaced by Wolves' Wayne Hennessey at half-time. Toshack paired Simon Church and Ched Evans together up front while Jack Collison played the advanced role normally filled by Ramsey.
It was 15 minutes before their first chance of note as Collison cut inside to create a shooting opportunity inside the box but his drive was deflected for a corner. Captain James Collins got his head to the resulting set-piece but his effort was beaten away by Eddie Gustafsson.
After that Sweden began to get on top and Wales had a let-off midway through the first half when Toivonen found the net with a header only to be ruled offside. Sweden went close again as Larsson curled a free-kick narrowly wide.
Sweden finished the first half strongly, Elmander breaking clear and forcing a low save from Myhill. He did even better from the resulting corner, controlling a bouncing ball with his chest and firing sweetly past Myhill.
Toshack replaced Myhill with Hennessey at half-time and also brought on Nottingham Forest's Earnshaw for Evans. Earnshaw was straight into the action and attempted to curl a shot into the bottom corner but his effort took a deflection and Collison was unable to turn it in.
Earnshaw brought a good save from Gustafsson on the hour after Sweden failed to clear a corner, the substitute hitting a powerful left-foot shot that the visiting custodian showed great agility to palm away.
Sweden came back late on, with Larsson stabbing an effort wide from distance and Tobias Hysen forcing Hennessey to save at full stretch from a Viktor Elm cross. Toshack said: "We were beaten by a better side, a more experienced side. I think the 1-0 scoreline could have been even worse."