In truth, the Iberians' quest for automatic qualification always seemed a long shot as it required a defeat for Russia away in Azerbaijan with a seven-goal swing.
Paulo Bento's side struggled to break through the Luxembourg rearguard early on but were helped by the sending-off of Aurelin Joachim for his high tackle on Andre Almedia just before the half-hour.
Portugal nabbed a second goal on 37 minutes when Moutinho's clever back heel reached Nani, who volleyed past a helpless Joubert.
Fabio Coentrao thought he had scored a third before the interval when Moutinho yet again cut the Luxembourg defence open and the left-back finished neatly only for the assistant referee to flag for offside.
It took until the 78th minute for Portugal to score again when Nani's corner was cleared only to Helder Postiga, whose thundering effort found the back of the net and rounded off the win.
The win was in vain as Russia secured a win to top Group F.