Danny Wilson's debut goal after 24 minutes took the pressure off before Kris Commons and Jamie Mackie both scored their first goals in a dark blue shirt to have the game finished by the break, with the second half a non-event.
Scotland will face tougher tests when they resume their Euro 2012 qualifying campaign next September with the double-header against the Czech Republic and Lithuania at Hampden, even though they will probably have most of their top players back from injury.
However, as a confidence booster if nothing else, this victory was welcome.
Levein had left several regulars out of his original squad for this less-than-glamorous friendly and was then hit by nine withdrawals which cast further doubt on its credibility.
The Scotland boss, though, was adamant opportunities were there for other players including 18-year-old Liverpool defender Wilson and Aston Villa midfielder Barry Bannan who both made their debuts.
In a side unrecognisable from the one which lost to Spain at Hampden in their Euro 2012 qualifier in October, defenders Steven Caldwell and Stephen Crainey returned from the international wilderness as Mackie started as the main striker, flanked by Commons on the right and Shaun Maloney on the left.
However, the Scots still looked too strong for the visitors.
The Faroe Islands' three British-based players, goalkeeper Gunnar Nielsen of Tranmere, Joan Simun Edmundsson of Newcastle and Ross County defender Atli Gregersen, were all playing, the latter as captain.
The home fans who made up the overwhelming majority of the 10,873 crowd were almost shocked in the eighth minute when Jann Ingi Petersen rattled a free-kick from 25 yards off the crossbar, the ball taking a nick off Commons to hand the visitors a corner which came to nothing.
That stung the Scots into action and Maloney's inswinging cross from the left found Commons unmarked at the back post but his header across goal found no takers.
In the 23rd minute Bannan, growing into the game, slipped the ball to skipper Darren Fletcher who drew a fine save from Nielsen with a low drive and the rebound was gratefully cleared behind by the visitors.
From Charlie Adam's corner from the right, Wilson escaped his marker at the back post to volley in from four yards.
The early Scottish nerves melted away and in the 31st minute Levein's men doubled their lead, again from a corner from the right. Adam's first attempt was repelled straight back to him but his second cross reached Commons at the near post and the Derby player scored with the neatest of flicks.
The visitors already looked shot and moments later Bannan crashed a left-footed drive off the base of the post.
A minute from the break the Villa midfielder, who had moved over to the right, swung in a deep cross which came off Wilson at the back post straight into the path of Mackie who gleefully blasted in from two yards.
The match was finished as a contest.
In the 48th minute Crainey's powerful 30-yard shot was knocked away by Nielsen, moments before Mackie drove wide from the edge of the box.
Six minutes later Wigan midfielder James McArthur came on to make his debut for the injured Adam.
Play continued to flow towards the Faroes' goal and minutes later Bannan headed a Commons cross over the bar from just eight yards out when he should have at least worked the goalkeeper.
Dundee United defender Garry Kenneth came on for Wilson on the hour mark and moments later Scotland should have made it 4-0.
Seconds after being foiled by Nielsen, Maloney picked up a slack passback from Faroe Islands defender Erling Jacobsen but chipped wide from 12 yards.
More Scotland changes followed as the second half wound down.
Midfielder Craig Bryson, goalkeeper Cameron Bell, defender Steven Saunders and striker David Goodwillie came on to make their debuts for Fletcher, Craig Gordon, Phil Bardsley and Commons respectively.
By that point the tempo had left the game but there was time for Bell to make a decent save from Edmundsson.