While the Scots senior side have failed to record a win from five attempts in their quest to reach next summer's World Cup in Brazil, Billy Stark's youngsters opened their bid to earn a slot at the 2015 finals in the Czech Republic with three points.
The visitors were stuffy but debutant Hearts winger Jamie Walker finally broke their resolve with a strike in first-half stoppage time.
Tony Watt - who rejoined the squad on Friday after initially pulling out with an ankle knock - added a second just after the hour mark after the visitors got themselves in a mess with a pass back to keeper Steve Pfeiffer.
And a third goal was added seven minutes from time when Pfieffer again blundered by dropping the ball at the feet of Lewis Toshney to ram home into an empty net.
The Scots missed out on qualifying for this year's finals in Israel with defeat to Austria in their previous campaign but their failed bid did see them knock eight goals past Luxembourg in two one-sided meetings.
A glut of goals was therefore expected again but it was the minnows who came up with some early half chances, first skipper Dzenid Ramdedovic firing straight at Dark Blues keeper Jordan Archer from a free-kick and then Tom Laterza flashing a low cross across goal an instant too early for the arrival of team-mate David Turpel.
Scotland's first sight of goal came after 18 minutes as Dylan McGeouch, Fraser Fyvie and Walker linked up before the Jambos teenager rolled the back back for skipper Stuart Armstrong to fire wide from 20 yards out.
Toshney went closer on 33 minutes, however, with Luxembourg struggling to clear from a Scots corner.
When the home team worked it back to the Dundee defender on the edge of the box, he whipped a first-time shot towards the top right-hand corner but saw Pfieffer push it onto the post.
Toshney was inches away again five minutes later as he just missed out on providing a finishing touch at the back post to Clark Robertson's flick on from Dylan McGeouch's corner.
But with the last kick of the first half, Scotland finally struck. Luxembourg were penned in by another corner as Fyvie worked a quick short exchange of passes with Stuart Bannigan before clipping the ball to Toshney at the far post. His headed knockdown was perfect for Walker to volley into the roof of the net.
Scotland did not exactly go all out to extend their lead in the opening quarter hour of the second half and were, in fact, fortunate that Turpel first blazed over from substitute Ryan Klepp's lay off and then was tame with a second effort after cutting in from the right channel.
A second goal did arrive on 66 minutes and it was all but gift-wrapped by the Luxembourgers.
Watt cut in from the right to shoot but Pfieffer could only parry the ball in front of him. With time to blast clear, sub Giuliano Jackson instead opted to pass back to the grounded keeper and he inexplicably picked it up four yards from his own goal.
That left Finnish referee Dennis Antamo with little choice to award the indirect free-kick and Scotland gladly made the most of it as Armstrong's lay-off was battered through the onrushing wall of visiting red shirts and into the net by Watt.
And the win was sealed on 83 minutes when a free-kick by substitute Ryan Fraser - also earning his first cap - was dropped by Pfieffer, leaving Toshney to blast home the third into an unguarded net.