Despite missing Cristiano Ronaldo through suspension, Portugal enjoyed their biggest-ever win in a dominant display at Estadio Algarve - where Manchester United midfielder Bruno Fernandes produced a hat-trick of assists before netting a late goal himself.
Portugal's previous record was 8-0, which they achieved three times - twice against Liechtenstein (1994 and 1999) and once versus Kuwait (2003).
Germany's 13-0 thrashing of San Marino in 2006 remains the biggest-ever win in European Championship qualifying.
Goncalo Inacio opened the scoring after 12 minutes and a brace from Paris Saint-Germain forward Goncalo Ramo soon had the home side in complete control.
Inacio headed in a fourth in first-half added time from another pin-point delivery by Fernandes.
Roberto Martinez's side did not let up and, just before the hour, Fernandes found Liverpool forward Diogo Jota, who raced clear to fire home a fifth.
Ricardo Horta added a sixth with 20 minutes left before Jota slotted in again. Fernandes then capped his fine individual display with a well-taken goal late on and Joao Felix completed the rout to make it six wins from six.
"It was a satisfactory aspect that, being 4-0 or 5-0 up, the team kept playing the same way as if it was 0-0," Martinez said.
"When you get that, it shows you the values of the players and that the respect toward the team is essential — that was really good to see."
The result matched the biggest-ever loss for Luxembourg, who have 10 points and are third, three points behind Slovakia.
The Slovaks remain five points behind Portugal after they made a fast start to beat Liechtenstein 3-0 in Bratislava with goals from David Hancko, Ondrej Duda and Robert Mak inside the first six minutes.
Elsewhere, Alfred Finnbogason scored in added time to give Iceland a 1-0 victory over Bosnia-Herzegovina in Reykjavik.
Croatia moved top of Group D after a 1-0 win in Armenia, where an early strike from Andrej Kramaric proved enough for all three points.
Wales beat Latvia 2-0 in Riga to boost their hopes of reaching next summer's finals in Germany, now three points behind Turkey.
Captain Aaron Ramsey scored his 100th career goal with a first-half penalty and David Brooks wrapped things up in added time to leave Latvia winless from five games.
With Reuters & AP.
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