Sunderland's relegation fears deepened on Merseyside as Idrissa Gana Gueye condemned them to defeat.
The Black Cats were second best throughout, even if Jermain Defoe rocked the crossbar moments before the Belgian striker settled it with ten minutes to play.
Sunderland had improved after the break, Everton switching off after an opening period in which they were sharper, more threatening, and in complete control of proceedings.
Lukaku's goal was a moment of infuriating naivety from the visitors, switching off after the best move of the game and leaving the awesomely powerful striker free to rampage towards goal and score.
It leaves David Moyes' side further adrift at the bottom ahead of the visit from Manchester City next week.
Even from the off, it was clear the Blues had the advantage in pace and possession.
Bryan Oviedo was struggling down the left flank, Seamus Coleman and Tom Davies both beating him too easily. The Black Cats were grateful that the hosts were unable to exploit a number of corners, though on the 12th minute Lukaku almost poked home at the back post as Oviedo and then Adan Januzaj failed to clear.
Ademola Lookman had already gone close, Jordan Pickford spilling his weak drive towards his own goal, recovering just in time to prevent it crossing the line.
In the 12th minute there was a almost a penalty, Coleman advancing towards the byline. Fabio Borini brought him down by Stuart Atwell got the call just right, the foul occurring just outside the box and a free-kick won.
Idrissa Gana Gueye came within inches of breaking the deadlock five minutes later, catching Billy Jones and Lamine Kone off guard and strolling towards goal. He wont low and hard from a tight angle and Pickford was relieved to turn it just wide with his feet.
If there was some encouragement for Sunderland, it was that the Blues began to labour on the ball and the home crowd began to get restless. There will little danger for Joel Robles in the Everton goal but Oviedo was improving and the Black Cats were finally getting some rtime in opposition territory.
But they let Coleman in down the right, and his low cross was excellent. Gueye ran onto it with a superb, sweeping, first time finish and from there they laid siege in the run-up to half-time. Ross Barkley had an effort pushed wide by Pickford before Tom Davies crashed the post with a stunning half-volley.
The second half was better right from the whistle, Everton sluggish and Jermain Defoe, largely a passenger in the first half, twice almost breaking clear. A clever move saw Fabio Borini have a strong effort deflected wide by the covering Ashley Williams.
A superb, and belated, corner from Seb Larsson, found Billy Jones leaping highest but his deflected effort was easily claimed by Joel Robles.
Everton were a shadow of their first half selves but there daunting flickers on the counter, Coleman twice wasting opportunities as he flew in behind the back line undetected. The introduction of Kevin Mirallas further increased the Blues breakaway threat.
The noise from the way end went up a notch, the restlessness on the home terraces noticeable.
All could see that the hosts had switched off, sloppy and unstructured. The key question was whether Sunderland had the quality to exploit it, and Mirallas should have killed the game when he ran untracked into the box, his meek effort crawling wide.
Ross Barkley was presented with a similarly excellent opportunity, Coleman again getting to the byline and crossing well. Unlike Gueye in the first half, Barkley could only hammer over the bar.
All of a sudden Sunderland were leggy, not able to get close to Lukaku as he drilled straight at Pickford from distance. The Belgian then surged away from Kone, drawing a fine save from Pickford.
Then, two minutes that settled the game.
Sunderland finally sprung a fine counter, Adnan Januzaj releasing Defoe. He shifted the ball well and his effort, beating Robles but dropping off the underside of the bar. Then from the corner, Lukaku left standing unmarked on the half way line. Everton moved it quickly and released him. From there the goal was inevitable, even if it needed a deflection to creep in.
That was game over, Wahbi Khazri and George Honeyman introduced before the fateful corner and therefore unable to make an impact. From there it was a case of how many Everton would score, Enner Valencia denied when through one on one with Pickford.