Scotland Under-21s kept alive their European qualifying hopes with second-half goals at St Mirren Park to win 3-0.
Billy Stark's side struggled to break down a stubborn Luxembourg side in the first half but stepped up the tempo after the break and Stuart Armstrong and Leigh Griffiths netted within five minutes of each other.
Substitute Tony Watt scored a late penalty and Scotland now travel to Austria looking for the 16-point total they are expected to need for a play-off spot.
The victory leaves unbeaten Scotland three points behind Group 10 leaders Holland and four clear in second place. Scotland need Austria to beat Holland in Tilburg on Friday night in order to have any chance of topping the group. Scotland would do so if they won their last game as they have a better head-to-head record against Holland.
Anything but an Austria win would guarantee Scotland second place but Stark believes they still need to win on Monday to be one of the four best runners-up that qualify for the play-offs.
Luxembourg were shutting out their hosts early on and they almost took the lead in the 25th minute. Tottenham goalkeeper Jordan Archer, making his first start amid injuries to Mark Ridgers and Grant Adam, dived full length to push wide Billy Bernard's header following a free-kick from the right.
Scotland were struggling to get the ball into the box, though Johnny Russell saw a long-range effort comfortably held before Danny Wilson curled over after a corner was half-cleared. Stark's team managed to push men forward in the closing stages of the half but were still lacking a cutting edge.
It was perseverance that finally broke down the visitors in the 63rd minute. The away defence closed down Griffiths after a one-two with Scott Allan but Russell ran in and tried a first-time shot that broke off a defender and spun across the 18-yard line. The ball fell kindly for his Dundee United team-mate Armstrong, who curled the ball into the roof of the net.
Scotland soon doubled their lead when Russell broke down the left and cut the ball back for Griffiths to sweep home from eight yards.
Luxembourg had a penalty claim denied when referee Thorvaldur Arnason ruled Wilson got the ball in a risky slide tackle on Tom Laterza. Arnason pointed to the spot at the other end when Watt's shirt was pulled just inside the box and the Celtic striker sent Philippe Hahm the wrong way in the 83rd minute.