Bruno Fernandes ran the show for Portugal as they romped to a record 9-0 win over Luxembourg on Monday without suspended talisman and all-time top goalscorer Cristiano Ronaldo.
Roberto Martinez's side have now won all six of their qualifying games, without conceding a single goal and scoring 24 themselves, with this the country's largest ever victory.
Portugal lead the Group J standings, five points clear of Slovakia in second place, whom they beat in Bratislava on Friday. Luxembourg are third, three points behind Slovakia.
Manchester United playmaker Fernandes, who scored Portugal's winner against Slovakia, laid on three goals as the Selecao filled their boots and scored one himself.
Goncalo Ramos, Diogo Jota and Goncalo Inacio struck two goals each, while Ricardo Horta and Joao Felix also scored.
Martinez, who replaced Fernando Santos after the Qatar World Cup, has a 100 percent record at the helm to date.
"We are still at the beginning of a new era with a new coach and we are still taking on board the coach's ideas," said Jota.
"Today we set a reference point match (to look at in) the future."
Sporting Lisbon defender Inacio sent the hosts ahead in the 12th minute with a header from Fernandes' exquisite cross with the outside of his foot.
Paris Saint-Germain striker Ramos drilled home the second five minutes later after Fernandes pressed high to win the ball back.
The 22-year-old striker then grabbed another goal in the 33rd minute with a clever turn and clinical finish for his sixth goal in eight appearances for his country.
Liverpool striker Jota hit the crossbar as Portugal dominated at the Algarve stadium near the country's south coast.
Inacio headed home his second goal from another Fernandes cross on the stroke of half-time and Jota struck early in the second half for the fifth, set up by the Red Devils midfielder again.
Portugal thrashed Luxembourg 6-0 in their first clash in the Grand Duchy and Horta rifled home from the edge of the box for their sixth of the night to match the haul.
Jota, who set up Horta, walloped home the seventh as Portugal continued pushing on without remorse, and Fernandes capped his virtuoso display by netting the eighth.
That matched their previous best win, 8-0 on three occasions, but substitute Felix struck a superb ninth from the edge of the box to set Portugal's new record.
"We have a great group of players, we take every game very seriously," said Horta.
"We're on the right track, but we have things to improve. Against Slovakia we played a game that was not at the level this team (can offer)."
Martinez's side can qualify for Euro 2024 on October 13 if they beat Slovakia and Luxembourg fail to beat Iceland.