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, amongst others, lacked sparkle early on but their overall efforts offered encouragement for the 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 after failing to qualify for the World Cup for the first time since 1998, but they still boasted plenty of know-how.
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.
Yet the match had a low-key feel to it with empty stands at either end, a crowd of just 8,258 and a subdued atmosphere.
In-form Hull goalkeeper Boaz Myhill was handed the number one jersey but then replaced by Wolves' Wayne Hennessey at half-time.
Toshack's controversial decision to omit Bellamy again saw youngsters Simon Church and Ched Evans paired together up front while Jack Collison played the advanced role normally filled by Ramsey. Fulham's Simon Davies won his first cap for almost a year.
Wales shaded the early possession but created little of note aside from a run by Church to the byline which resulted in a cross being easily claimed by goalkeeper Eddie Gustafsson.
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 Gustafsson.
After that Sweden began to get on top and Wales had a let-off midway through the first half as Elmander held the ball up and found former Wanderers player Christian Wilhelmsson out wide.
Wilhelmsson picked out Toivonen with his cross but the PSV Eindhoven striker's header was ruled out for offside - much to his surprise, having started celebrating the goal.
Sweden went close again after winning a free-kick 25 yards out 10 minutes before the break but Birmingham's Sebastian Larsson curled narrowly wide.
Collison tried his luck again from distance but shot well over and Sweden finished the first half strongly.
Elmander broke clear and forced a good low save from Myhill.
He then did even better from the resulting corner, controlling a bouncing ball with his chest and then 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.
Wales then enjoyed a good spell with Bale growing in influence on the left and getting forward at every opportunity.
Earnshaw also appeared to enliven the attack and brought a good save from Gustafsson on the hour.
Sweden struggled to clear a corner and Earnshaw struck a powerful left-foot shot amid the goalmouth scramble but Gustafsson showed great agility to palm away.
As is usual in friendlies, the changes then began to come thick and fast with Sam Vokes, David Cotterill, Lewin Nyatanga and Andrew Crofts all introduced. Bale and Collison were among those to make way.
Sweden came back late on, with Larsson stabbing an effort wide from distance and Tobias Hysen, son of former Liverpool defender Glenn Hysen, forcing Hennessey to save at full stretch from a Viktor Elm cross.
Elm then saw another long-range effort take a deflection and loop over the defence but Hennessey touched over the bar.
Oscar Wendt had a shot deflected narrowly wide for a corner and Elm's next effort was also blocked.