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 were condemned to their 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 their 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 their home defeat to Hull City.
The hosts started brightly, 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 team-mate 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 they 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.
And the 20-year-old had a key impact once again as Everton deservedly went two up, the striker playing 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 the interval when Lukaku bagged his second of the game.
The former Anderlecht man capitalised on confusion in the Newcastle defence to latch on to a goal kick from Tim Howard, collecting the ball ahead of Krul before rounding Fabricio Coloccini and tucking the ball into an empty net.
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 - they 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 defence, but it was Pardew's side who dictated the majority of the play in the second period.
And Newcastle threatened 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 clung on to seal victory.
