Roberto Martinez's visitors made a flying start during a frenetic first half, with Lukaku sliding in to put them ahead in just the second minute.
Phil Jagielka did well to maintain that advantage when he cleared Dwight Gayle's clever chip just two minutes later, but despite plenty of opportunities, the hosts were unable to level before half-time.
Palace, without club captain Mile Jedinak and in-form winger Yannick Bolasie due to the duo's international duties at the Asian Cup and Africa Cup of Nations respectively, looked brighter after the restart, but they failed to fashion any clear openings during a low-key second half.
Everton could have wrapped the points up 13 minutes from time when Lukaku just failed to connect with Aiden McGeady's cross.
The visitors returned on Tuesday from a six-day training camp in Qatar, and that break seemed to have rejuvenated Martinez's side when they made a stunning start - Lukaku putting them ahead just two minutes in.
Damien Delaney's poor attempt at an interception allowed Steven Naismith to break into the box and when the Scot drilled a low cross towards goal, Julian Speroni could only parry the ball straight into the path of Lukaku, who bundled home.
Palace were almost level just two minutes later when Gayle managed to squeeze an effort past Joel Robles, but Jagielka recovered superbly to scoop the ball off the goal-line.
Pardew's side continued to press and, as Everton struggled to cope with Marouane Chamakh's presence up front, the Moroccan was only denied an equaliser when John Stones blocked his venomous strike.
Unfortunately for Palace, Chamakh's game was cut short soon afterwards when he was taken off on a stretcher after suffering a suspected broken nose following a collision with Seamus Coleman.
Jordon Mutch, signed on Thursday, came on to make his Palace debut in place of the stricken forward, but he was unable to match Chamakh's impact as Everton retained possession well.
Palace became increasingly wasteful as half-time approached, and Everton were gifted the chance to double their lead when Naismith nipped in to claim the ball in midfield and found Lukaku, but the Belgian's touch was poor.
The hosts came out strongly after the interval and went close when Gayle whipped in a terrific cross towards Yaya Sanogo, but the Arsenal loanee failed to connect and the ball drifted wide.
Pardew introduced Wilfried Zaha in place of defender Martin Kelly as the clock passed the hour mark in a bid to add a spark to Palace's blunt attack, while Martinez brought on Bryan Oviedo.
Lukaku should have doubled his and Everton's tally in the 77th minute but he failed to latch on to McGeady's low pass across the face of goal.
Speroni then pulled off a superb save to deny McGeady before Lukaku fired another effort into the side-netting, as Everton secured the points.
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