Having won his first four games at the helm, returning hero Pardew was unable to inspire yet another comeback as Lukaku struck inside two minutes to claim all three points and hand Roberto Martinez and Everton their first Premier League victory since December 15.
Palace had won from losing positions in both of Pardew's opening league fixtures in charge but there was to be no rescue act here, despite a first-half rally following Lukaku's early effort.
Everton did not start like a team on a six-game winless streak but there were moments to suggest their season has not turned the corner just yet, despite victory in south London moving the Toffees seven points clear of the relegation zone.
Palace dominated for large periods of the game and it was only a lack of clinical finishing that saw them leave empty-handed.
But it was Everton who took the lead with what proved to be their only effort on target until the closing five minutes.
Steven Naismith picked up a perfectly-weighted through ball and saw his cross palmed away by Julian Speroni, with the rebound coming off the sliding Lukaku to open the scoring.
But the hosts, who battled back after going behind in their last league outing at Burnley, were unperturbed by falling behind so early and looked to peg Martinez's side back immediately.
The recalled Dwight Gayle came close to levelling moments later, beating Everton goalkeeper Joel Robles to the ball before lifting an effort towards goal, only to see Phil Jagielka hack clear just in time to prevent an instant reply.
Yaya Sanogo, making his home debut for the Eagles, also had a good chance as Everton failed to clear the resulting corner but his low shot was blocked and Marouane Chamakh was the next Palace player to test the Toffees' back-line, cutting inside before seeing his effort deflected behind.
That was Chamakh's last meaningful involvement as a clash of heads with Seamus Coleman left the Morocco international with a bloody nose - with debutant Jordon Mutch coming on in his place.
Puncheon stung the palms of Robles as Palace continued to be the side who were carving out chances as the first half wore on, with Mutch and Puncheon both firing over in stoppage time.
The Palace momentum was disrupted by the half-time rest and they could not start the second 45 minutes with the same vigour as the quality of the final ball into the box kept falling short.
Sanogo was inches away from connecting with Gayle's deep cross before the former Peterborough forward shot high and wide.
Wilfried Zaha was introduced on 65 minutes and instantly won two corners for the Eagles, with Glenn Murray also brought on by Pardew in the hope of rescuing something from the game.
Having soaked up a lot of pressure, Everton broke clear with 10 minutes remaining but Lukaku could not get a telling touch to Aiden McGeady's driven cross.
With Palace throwing men forward, Everton looked to take advantage and McGeady drew a smart save from Speroni before Lukaku fired into the side netting shortly afterwards.
Republic of Ireland international McGeady wasted another good chance to seal the win in stoppage time but Palace failed to muster a late flurry, with Robles largely untroubled in the second half.
Source : PA
Source: PA