The striker now has three goals in four games for his adopted country.
Here, Sports Mole takes a closer look to see if the result was fair.
On target 7
On target 3
Was the result fair?
Yes. Scotland were far from impressive, but they still deserved to win.
4/10. They're not the best team, but they are only part-timers. They were much better in the second half and could have scored an equaliser. Mario Mutsch was Scotland's biggest threat from left-back, but they had very little else in their arsenal. Lars Gerson's free kick is a highlight, though. It was a brilliant strike and he can be very pleased with that goal.
5/10. Scotland lacked fluidity and their passing wasn't incisive. They looked comfortable in the first half, but didn't really spark going forward against weak opposition. They had a bit of chasing to do in the second half as Luxembourg enjoyed more of the ball. It was a fairly laborious evening, all things considered.
Sports Mole's man of the match
Jordan Rhodes: He scored both goals, and nearly had a third. There's no doubt that he deserves this award.
Cyril Zimmerman had an easy game. There was no passion, and nothing at stake. Neither team made a bad tackle.
Luxembourg: The tiny nation hosts Azerbaijan in a World Cup qualifier on February 22.
Scotland: Estonia visit Pittodrie for another friendly on February 6.