Goals from Zlatan Ibrahimovic, Emir Bajrami and Ola Toivonen gave the home side a deserved victory, with Levein no doubt hoping more of his experienced campaigners will be back in action for next month's Euro 2012 qualifiers against Lithuania and Liechtenstein.
With six call-offs ahead of this match, and having already suffered the loss of first choice goalkeeper Craig Gordon and defender Gary Caldwell, the national team boss named what was probably a more experimental side than he would have hoped for ahead of that crucial double-header.
There were no real surprises in the line-up, as Allan McGregor made his first Scotland appearance in 17 months when he started in goal. The Rangers number one was initially banned from the national team for his role in the "Boozegate" affair last year but has returned under Levein.
Garry Kenneth and Christophe Berra started in the heart of defence in the absence of injured duo Caldwell and Andy Webster, while Steven Fletcher was handed the lone striker role with Kenny Miller struggling with shin splints.
Sweden were boosted by the return of talismanic striker Ibrahimovic, who has come out of international retirement to boost their own hopes of qualifying for Euro 2012.
Levein had urged fans not to boo McGregor and, despite the controversy surrounding his return, he was given a positive reaction from the 2,000 travelling fans when his name was called out by the PA announcer ahead of kick-off.
Unfortunately for the goalkeeper, his first task was to pick the ball out of the back of the net when the home nation surged into the lead with just four minutes gone.
Pontus Wernbloom supplied a lovely pass from the right to Ibrahimovic and it was all too easy for the Barcelona striker to rifle past the outstretched hands of McGregor from 12 yards.
Sweden were threatening again when Toivonen tried his luck from the edge of the box but his deflected shot was blocked by McGregor, who was unable to hold the effort and looked on in relief as Johan Elmander fired wide from the rebound.
The Tartan Army reacted with fury when Kirk Broadfoot was booked for a challenge on goalkeeper Andreas Isaksson but they could have been celebrating just moments later.
James McFadden whipped a dangerous cross in from the left, which Isaksson failed to hold, and the ball fell for Adam only for the Blackpool midfielder to scuff his shot wide of target.
But it was Sweden who found the back of the net again six minutes from half-time. Bajrami's angled drive was blocked by McGregor but fell kindly for him to have another go and he hooked a superb right-foot shot into the top corner.
The home side added a third in controversial circumstances after 54 minutes when Bajrami's cross from the left appeared to swerve over the line but play continued and Toivonen was first to the ball to squeeze a header between two Scotland defenders and into the back of the net.
Scotland had already replaced Kevin Thomson with Scott Robertson and, with just over an hour gone, Kris Boyd and James Morrison were thrown into the action as the visitors attempted to haul themselves back into the game.
Boyd immediately had the chance to pull a goal back when he met a Darren Fletcher cross only for his point-blank shot to be blocked by the legs of Isaksson.
McGregor prevented the Scots from falling further behind when he produced a one-handed save to swipe a close-range effort from Christian Wilhelmsson to safety.
At the other end, Boyd picked up a short pass from Chris Iwelumo but was again denied the sight of the net bulging as he blasted over the crossbar this time.
The result did little to dampen the spirits of the vocal travelling fans but the performance will give Levein plenty to ponder ahead of his first competitive match in charge in Kaunas early next month.