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.
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.
Newcastle could not get to grips with the hosts’ high-tempo start, with Lukaku heavily involved in almost every attack.
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.
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.
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.
