Tuesday's game had become somewhat of a formality with Portugal sat three points behind Russia, who picked up a group-winning point at fourth-placed Azerbaijan, following a disappointing 1-1 draw away to Israel on Friday.
After managing to keep Portugal out for almost half an hour, the visitors' task was made near impossible by Aurelien Joachim's red card, with Silvestre Varela and Nani hitting a quick-fire double to move Portugal ahead.
With the hosts having little to play for, Luxembourg rallied in the second half, but they were put to bed by Helder Postiga's late third.
Paulo Bento made five changes to the side held by Israel, while Nani was named captain in the suspended Cristiano Ronaldo's absence.
Visiting goalkeeper Jonathan Joubert saw Varela head over in just the third minute and had to be alert after saving Nani's long-range effort to tip away Postiga's follow-up.
Postiga had the ball in the net, but was called offside, Fabio Coentrao nodded onto the crossbar and Nani's header was fantastically saved by Joubert as Portugal turned the screw.
Lars Krogh Gerson had the visitors' brightest moment just after the hour mark with a sweetly struck half-volley, but it was straight at Rui Patricio.
That perhaps gave Luxembourg confidence and the Sporting Lisbon keeper was forced to scramble across his goal to see Tom Laterza's ambitious shot from the right touchline wide.
But Portugal wrapped up the win in the closing stages, substitute Hugo Almeida flicked Josue's cross to Postiga, and the Valencia striker slotted underneath Joubert to give the hosts confidence heading into November's play-offs.
