The irrepressible Belgium international, the club's $56 million record signing, was not to be denied after twice hitting the frame of the goal prior to Scott Dann's 76th-minute header giving the visitors the lead.
In-form Lukaku made it seven goals in his last six matches nine minutes from time to prove, once again, just how valuable he is to Roberto Martinez's side.
It was no surprise he benefited from a cross from fellow 21-year-old Gerard Deulofeu as the Catalan had provided five previous assists for his team-mate and is the first person he looks for when he receives the ball out wide.
As a result Everton are more direct in the final third this season as Deulofeu's preference to beat his marker and whip in crosses is matched by his ability to drive at the heart of defences to create a different problem.
Everton had scored seven in their last two league matches, Palace five in 90 minutes against Newcastle, but if the watching Wayne Rooney, whose last Premier League goal came against former club Everton in mid-October, was expecting a glut he was disappointed.
He cannot fail to have been impressed by Lukaku, however, who has become the focal point of this Everton team with Arouna Kone, the smaller half of a little-and-large combination up front, developing a good understanding with his partner and Ross Barkley also knowing how to get the best out of the Belgian.
But for all their probing they drew a blank in the first half, although Lukaku was unlucky not to score his seventh goal in six matches when his shot beat goalkeeper Wayne Hennessey but rebounded off the inside of the far post and flew across the face of goal.
But he is not just an out-and-out powerhouse striker and his cushioned lay-off set Deulofeu and Kone racing through for a two on one against Dann only for the former Barcelona graduate's touch, which had just seen him pull off a drag-back nutmeg through Yohan Cabaye's legs, let him down.
Palace have their own big man up front in Connor Wickham and his near-post header from a corner forced Tim Howard into a point-blank save but the first half was mainly a tale of final touches not coming off as Barkley and Kone both shot into the Park End.
Howard's legs came to the rescue again after the break to deny Yannick Bolasie on the breakaway while Dann's blushes were spared only by the crossbar as he headed Barkley's inswinging free-kick past Hennessey, who brilliantly tipped over Tom Cleverley's drive.
Liverpool fan Dann thought he had completed a memorable Merseyside double - having scored the winner at Anfield a month ago - when he nodded in from a corner after losing marker Gareth Barry but Lukaku, who also crashed a volley against the crossbar, had the final say with nine minutes to go.
Key Opta stats:
- Everton are unbeaten in their last 16 Premier League games played on a Monday (W7 D9).
- Crystal Palace have scored the highest proportion of goals from set-pieces this season in the Premier League (45 per cent).
- Romelu Lukaku has scored in each of his last three Premier League appearances against Crystal Palace.
- Palace have won more points away at Everton (13) than they have away at any other team.