Bernardo Silva, Cristiano Ronaldo and Goncalo Guedes were on target as Portugal closed on a spot at Euro 2020 with a comfortable 3-0 win over Luxembourg.
Manchester City midfielder Silva scored the easiest of openers 16 minutes into Friday's Group B clash in Lisbon and Ronaldo's excellent chip in the second half doubled the lead.
Substitute Guedes added late gloss and in truth, the European champion should have won by a bigger scoreline, with Ronaldo uncharacteristically profligate prior to his goal.
Still, Fernando Santos' men were rarely troubled in the capital and, with a four-point buffer to third and just three games remaining, Portugal took another step towards qualification.
Ronaldo cleared the crossbar with an early long-ranger and Joao Felix fired wastefully wide on the half-volley from eight yards as Portugal flew out the blocks.
The inevitable breakthrough arrived when Nelson Semedo's cross ricocheted off goalkeeper Anthony Moris and allowed Silva to easily slot home.
It remained one-way traffic in the second half, with Bruno Fernandes' stinger preceding an audacious overhead-kick from Ronaldo, who also saw a bending effort well saved by Moris.
Ronaldo finally had his goal when he pounced on Maxime Chanot's woefully mishit backpass and lofted a delightful chip over Moris.
The Juventus forward had already seen a couple of penalty claims waved away and was unlucky another was not given when he was hacked by Leandro Barreiro Martins.
Ronaldo prodded another effort wide and saw a header cleared off the line but Guedes fired through a crowd of bodies in the final minute to increase the scoreline.
What does it mean? Portugal one step closer
Luxembourg was unlikely to provide a genuine challenge and so it proved against a Portugal side which really should have won by a wider margin. With a four-point gap to third-place Serbia a place at Euro 2020 is edging ever closer.
Fernandes sets the tempo
Fernandes was pick of the host's midfield, setting the tempo and serving as the chief creative force from deep, with Silva and Joao Felix also lively.
I Chanot believe you did that!
Before his goal, Ronaldo was enduring a bit of a miserable evening with the shooting boots but he needed no invitation when Chanot left his side in a spot of bother. It cost Luxembourg any hope of stealing an unlikely point.
Portugal will aim to close the gap on leader Ukraine when it travels to Kiev on Monday. Luxembourg faces a friendly with Denmark a day later.