Gonaclo Inacio, Goncalo Ramos and Diogo Jota all claimed braces with Bruno Fernandes, Ricardo Horta and Joao Felix also on target at the Estadio Algarve.
It served as Portugal’s biggest ever margin of victory, surpassing the former record 8-0 scoreline they had chalked up three times previously.
The triumph also made it six wins out of six in Group J for table toppers Portugal who are five points clear of Slovakia and stay firmly on course for qualification for next summer’s Germany showpiece.
Dias played for the full game while Bernardo figured for an hour before making way with City colleague Joao Cancelo – currently on loan at Barcelona – coming on as a second half substitute
Roberto Martinez’s men made a flying start, racing into a two-goal lead inside the first 20 minutes.
First Inacio headed home from Bruno Fernandes’s inviting cross on 12 minutes.
Then, just five minutes later, an inviting Bernardo assist set up Ramos who doubled Portugal’s advantage.
The hosts’ dominance was further emphasised just past the half with Paris Saint-Germain star Ramos adding his second and Portugal’s third with a superb strike.
On the cusp of half time, Sporting CP defender Inacio followed suit by securing his own double and the hosts’ fourth goal with Fernandes again the supplier.
There was no respite for Luxembourg after the break.
Portugal added a fifth goal on 57 minutes through Liverpool’s Diogo Jota before Braga forward Ricardo Horta’s 67th minute effort brought up the half dozen.
Jota then became the third player to bag a brace 13 minutes from time as Portugal racked up a magnificent seven.
The scoring wasn’t over there with Fernandes also getting in on the act six minutes from time to further extend an emphatic rout.
And Luxembourg’s misery was compounded two minutes from time when substitute Joao Felix also found the target to seal a new national record.
Martinez’s side resume their campaign next month with a game against Slovakia before then travelling to Bosnia-Herzegovina.