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
Belgium's creativity and power prove too much for World Cup debutants Panama as the Group G favourites overcome the heroics of goalkeeper Jaime Penedo and a massed defence to run out 3-0 winners on Monday.
Manchester United manager Jose Mourinho is confident Romelu Lukaku's problems in front of goal will come to an end -- just as soon as he secures a new boot deal.
Manchester United striker Romelu Lukaku enters a not guilty plea after being cited for holding a rowdy party at his rented Beverly Hills mansion in July.
Manchester United striker Romelu Lukaku trolls Cristiano by commenting ‘Messi is better mate’ on the Real Madrid player’s instagram post.
Belgian international Romelu Lukaku grabs his second goal in his second start for United as the Red Devils ease past a disjointed City at Houston's NRG Stadium.
Romelu Lukaku bags his first goal in a Manchester United shirt as the 10-man Premier League giants labored to a 2-1 victory over Real Salt Lake in Utah.
Romelu Lukaku bids a fond farewell to Everton as he contemplates life with Manchester United following his move for a reported £75 million ($97m, 85.5m euros) transfer record deal between British clubs.
Manchester United announce that they reached an agreement with Everton for Romelu Lukaku, who is set to join the club for a reported £75million ($97m, 85.5m euros), a record fee between British clubs.
Manchester United agree a fee of around 75 million pounds ($96.98 million) to sign striker Romelu Lukaku from Premier League rivals Everton, according to British media reports.
Romelu Lukaku is in line to finish the season as the Premier League's top scorer but the Everton striker is more concerned with helping his team win rather than gaining personal accolades.