Paulo Dybala picked out Lukaku with a clever cross as the Belgium striker headed Roma in front in the fifth minute at the Stadio Olimpico.
Bruno Fernandes and Ricardo Horta netted the goals for Roberto Martinez's Portugal, with Cristiano Ronaldo not on the scoresheet, to end with 10 wins from 10 matches in Group J.
Lukaku grabbed his third goal in five league games for Roma after latching onto a clever pass from Paulo Dybala midway through the first half.
Belgium forward Lukaku rolled in Roma's sixth in the 82nd minute of a dominating performance in which talisman Paulo Dybala also got off the mark for the season with a brace.
Romelu Lukaku completed his season-long loan move to Roma from Chelsea on Wednesday after being welcomed as a hero by supporters.
According to the Italian sports daily, Roma will pay the London club 5.8 million euros ($6.2 million) and the player will receive an annual salary of 7.5 million euros
The visitors had been rocked by a row between new coach Domenico Tedesco and veteran goalkeeper Thibaut Courtois in the build-up to the game, and made a slow start before Lukaku pounced with two close-range finishes towards the end of the first half
Thierry Henry said that it will be difficult for Romelu Lukaku to handle after he made some crucial mistakes in Inter's Champions League final loss against Manchester City.
Lukaku, on loan at Inter from Chelsea, has struggled with injuries and form this season, but has scored three goals in his last three games
Kevin De Bruyne’s mercurial talent is indisputable and Romelu Lukaku will be a powerful force up front, so the big question for Belgium heading to the World Cup in Qatar is whether they can get the best out of playmaker Eden Hazard.
Belgium coach Roberto Martinez says the absence of "irreplaceable" Romelu Lukaku from the World Cup would force his side to change the way they play, but the striker has not been ruled out of the tournament yet, team officials confirmed.
Romelu Lukaku has suffered a new hamstring injury less than a week after making his return to action for Inter Milan, the Serie A club said on Monday.
Romelu Lukaku should be available for Inter's Milan's Champions League clash with Viktoria Plzen which could seal the Italians' place in the last 16, coach Simone Inzaghi said on Tuesday.
Inter Milan made it two from two in Serie A with Saturday's comfortable 3-0 win over Spezia on Romelu Lukaku's return to the San Siro.
Forward Romelu Lukaku scored on his debut for Inter Milan as they made a flying start under new coach Antonio Conte with a 4-0 win over promoted Lecce in Serie A on Monday.
Ole Gunnar Solskjaer's Manchester United made it four wins out of four in the Premier League on Wednesday, beating Newcastle to close the gap on fourth-placed Chelsea, who were held at home by Southampton.
Football is played in cycles, although they do not change often.
"Everyone thinks Romelu Lukaku is just about goals, goals, goals, but I want to be seen as an all-rounder" says Lukaku.
Roberto Martinez reveals that Romelu Lukaku is an injury doubt for Belgium's World Cup blockbuster tie against England after the in-form striker picked up an ankle injury.