The Blackburn Rovers striker bagged two goals but it was a struggle in the second half as the hosts came back to give Billy Stark's men a real scare in a match lacking in quality
The hosts may be a landlocked country, but their defence in the opening 25 minutes resembled something like the parting of the Red Sea as Jordan Rhodes, who scored a hat-trick for the Under 21's at the Josy Barthel Stadium last time, helped himself to a double.
But Lars Gerson then gave the Scots a fright straight after half-time as he got Luc Holtz's side back into the game with a stunning free-kick from 25 yards.
And though the Scots seemed in a comfortable position in this match after their dominant first half display, they ended up holding on for a result.
A half-empty stadium and the lamenting sound of both teams' national anthems before the game did little to inject any excitement into the encounter, but the visitors started brightly and the away fans were almost on their feet as Rhodes found himself through on goal in nine minutes, but did not connect properly with the chance.
However, that gave the Scots confidence and Rhodes soon capitalised on some dodgy defending, hitting home from a yard out after some pinball following a teasing ball in from Paul Dixon. It was not worthy of Fifa's Puskas Award but it gave the visitors the initiative in the match.
Luxembourg responded through Mario Mutsch, who got on the end of a cross which goalkeeper Matt Gilks had to be aware of. The skipper had another chance a couple of minutes later as poor sloppy defending from Stark's men allowed him time and space but his shot drifted harmlessly wide.
However, Scotland doubled their lead on 23 minutes as Rhodes instinctively knew where to be as the ball landed five yards out and, after losing his man, lashed home following Andrew Shinnie's blocked shot.
The hosts did their best to mount a few attacks in the first half and although they got into some threatening positions they failed to trouble Gilks in goal.
However, a superb free-kick from Gerson got the hosts back into the match minutes into the second half after substitute Liam Kelly had been penalised for a foul. It was the first time they had scored against the Scots and arguably they will not net a better goal against them again, as Gilks was left helpless.
The strike seemed to lift the hosts and they continued to put more pressure on Stark's side with the visitors seemingly losing their way in the second half.
Griffiths was then introduced to the play as Scotland looked for some inspiration off the bench. The Hibernian striker has been on lethal form recently and earned his first cap here but it was the hosts who looked the more likely to score.
Kenny Miller had an effort at goal blocked but it immediately gave Luxembourg the opportunity to counter. Mutsch delivered a terrific ball in for substitute Stefano Bensi to power a header towards goal but the Scots keeper palmed away for a corner.
Luxembourg continued to create chances and if they had the guile of Scotland's new found hero in Rhodes, they might have even found an equaliser.
The Scotland No.10 was denied a hat-trick when his headed goal was adjudged to be offside but the hosts were not disheartened and Bensi tried his luck from 20 yards to test the Scots goalkeeper.
In the end the Scots held on but there is a plenty of work to do before their next World Cup qualifier in March.