The Belgian had gone nine games without a goal and was becoming a more peripheral figure since Ole Gunnar Solskjaer's appointment, while Marcus Rashford established himself as United's leading striker.
With Rashford not fit to start and Anthony Martial and Jesse Lingard also injured, United were without their entire first-choice front three.
But after recovering from missing a glorious chance Lukaku scored in each half to keep Arsenal, a point and a position above them in fourth, under pressure.
A further finish from Ashley Young, after Joel Ward had responded for 14th-placed Palace, ultimately ensured a continuation of the momentum they will hope to carry into next week's crucial Champions League fixture at Paris St Germain and perhaps next season's competition.
If Palace had taken confidence from United's dwindling options, which also meant rare starts for Fred and Alexis Sanchez, they too were vulnerable without the injured Aaron Wan-Bissaka and Mamadou Sakho.
Ward and Martin Kelly therefore respectively started at right-back and in central defence, and Lukaku should have taken advantage of the hosts' uncertainty as early as the eighth minute, when Luke Shaw's corner found him in space directly in front of goal but he somehow volleyed over.
The lively Andros Townsend twice threatened for Palace, when on both occasions he shot narrowly wide, before in the 33rd minute after Shaw again put him into space, Lukaku gave United the lead.
Fred had found Shaw on the left wing, and after he resisted challenges to carry possession into Palace's penalty area he laid off to Lukaku, who this time showed greater composure to take a touch before curling first time into the bottom right corner and beyond Vicente Guaita's reach.
Jeffrey Schlupp almost produced an immediate response when he glanced wide from close range but, if they remained in contention for a point, further poor defending undermined them as Lukaku extended United's lead in the second half.
Paul Pogba should already have scored with a header when, from a 52nd-minute corner, Palace were static as further headers from Chris Smalling and then Victor Lindelof found Lukaku, who under minimal pressure by the near post held off James Tomkins to smartly finish over Guaita.
The hosts' goal came through Ward in the 66th minute, when after Townsend was dispossessed, Schlupp collected the loose ball on the left and beat David De Gea by crossing to Ward at the back post, leaving the defender with the near-open goal into which he sent his diving header.
If Palace threatened a second through substitute Max Meyer, United were clinical in delivering their third, in the 83rd minute through Young.
Lukaku was again involved when exchanging passes with Pogba before the latter fed Young into space at the back post, and United's captain secured all three points by calmly finishing low beyond the beaten Guaita.
In stoppage time Ward kicked the ball from De Gea's grasp and in after a header from Christian Benteke, but referee Martin Atkinson rightly ruled it out.