The Belgian netted twice on his home debut and laid on another for Ross Barkley and, though Yohan Cabaye and Loic Remy responded, the damage was done
Lukaku - on loan from Chelsea - produced a magnificent performance in his first start on Monday to help maintain his side's unbeaten start to the top-flight campaign.
Newcastle was condemned to its second successive league defeat, as a first-half double from Lukaku, which sandwiched a goal from Ross Barkley, wrapped up the win for Everton.
Substitute Yohan Cabaye netted in spectacular fashion early in the second half before Loic Remy reduced the deficit further late on, but Newcastle could not complete the comeback despite its best efforts.
Everton made two changes to the side that started in the 3-2 win at West Ham last time out, with Lukaku - who scored the winner at Upton Park - and James McCarthy coming in for Nikica Jelavic and Steven Naismith. Meanwhile, midfielder Gareth Barry made his 500th Premier League appearance.
Newcastle boss Alan Pardew brought in Cheick Tiote and Yoan Gouffran in place of Cabaye and Papiss Cisse after the Magpies' home defeat to Hull City.
The hosts started brightly, with Lukaku putting the ball in the net in the first minute only to see the flag raised for offside. But just three minutes later, he did put Roberto Martinez's men ahead, as his Belgium international teammate Kevin Mirallas beat Davide Santon to a loose ball before delivering a superb right-wing cross that Lukaku duly placed past Tim Krul.
Everton continued to push forward following the goal, and the hosts twice came close to doubling their lead when Barkley fired wide from the edge of the area, before Krul denied McCarthy after the visitors had given the ball away inside their own half.
Newcastle could not get to grips with the hosts’ high-tempo start, with Lukaku heavily involved in almost every attack. The 20-year-old had a key impact once again as Everton deservedly went two up. Lukaku played a clever pass into the path of Barkley, who coolly slotted the ball into the bottom corner.
Pardew’s men were reeling by this point, and the home side looked to have sealed the three points eight minutes before halftime when Lukaku bagged his second of the game.
The former Anderlecht man capitalized on confusion in the Newcastle defense to latch onto a goal kick from Tim Howard, collecting the ball ahead of Krul before rounding Fabricio Coloccini and tucking the ball into an empty net. Howard became the second American goalkeeper in the Premier League to register an assist during the matchweek, following in Aston Villa keeper Brad Guzan's footsteps.
Newcastle rarely troubled Everton in the first half, but after Pardew made two changes during the interval - Mike Williamson and Cabaye were brought on for Mapou Yanga-Mbiwa and Hatem Ben Arfa - the club pulled a goal back almost immediately.
France international Cabaye fired a fine long-range strike into the top corner shortly after Gouffran had hit the post to give the visitors a glimmer of hope.
Everton responded well, with Lukaku spurning a chance for his hat trick after he had again found a way in behind the Newcastle defense, but it was Pardew's side that dictated the majority of the play in the second period.
Newcastle threatened for a dramatic comeback when Remy tapped in from close range after latching on to Mathieu Debuchy's flick-on in the 89th minute, but Everton hung on to seal victory.