David Moyes' Sunderland were largely out-classed by Everton this afternoon but did nearly salvage hope as Jermain Defoe went close late on at 1-0 - sport's narrow margins were painfully evident as his shot crashed off the underside of the bar minutes before Lukaku's crucial second.
Now three points from safety and still rock bottom Sunderland face Manchester City next, as they must improve to once again miraculously avoid relegation.
Sunderland fortuitously weathered an early storm with Everton immediately forcing the Wearsiders onto the back foot.
Mostly the Merseysiders attacked the Black Cats' left, with Bryan Oviedo fortunate to avoid a booking when he clipped Seamus Coleman down the Everton byline in the opening couple of minutes.
A plethora of early corners kept Sunderland pinned to edge of their 18 yard box , with Ademola Lookman nearly embarrassing the returning Jordan Pickford. Sunderland's stopper spilled the 19 year old's tame side footed effort, barely diving on the ball on second attempt, as it nearly squirmed into the goal.
Another Everton corner nearly lead to an early breakthrough with Lukaku unable to reach Ross Barkley's flat cross which evaded Adnan Januzaj at the near post.
The Blues' attack continued to target their former left back Oviedo, Borini nearly conceded a penalty fouling Coleman, covering for the Costa Rican. Gueye wasted the set play chipping harmlessly over inside the Sunderland area.
Everton's best early opportunity came from a Sunderland error, Billy Jones was caught in possession by Gueye, who drove on goal and nearly nutmegged Pickford. The England under 21 international just deflected behind, using his knees at the near post.
As Sunderland grew in confidence, more space opened up for their more talented opponents as was evident in Everton's breakthrough. An excellent switch from Tom Davies, gave Coleman license to attack Oviedo his cutback was smashed into the roof of the net by the on-running Gueye. The clinical opener left Sunderland a proverbial mountain climb, given the lack of goal threat they provide.
Just before the break Sunderland narrowly avoided going two down, Davies hit the outside of the post with a brilliant improvised effort. The rising star had Pickford beaten with his outside of the boot half volley in first half injury time.
The Mackems immediately upped their intensity as play resumed, winning a couple early corners to start the second half. Despite more intent and territory their best chance saw Jones head comfortably wide at the near post from a corner. Another corner saw Stuart Attwell wave away optimistic penalty shouts, the ball had deflected off Ashley Williams' arm but the Welshman was looking away, with Kone heading at him from point blank range.
The pattern of Everton dominating the ball and having a majority of possession and territory resumed after an initial ten minute spell of Sunderland pressure. Lookman wasted a deceptively good chance when he snatched on the half-volley straight at a red and white shirt, unmarked from a half cleared corner.
As the half wore on Sunderland showed a growing appetite to counter attack and get level but often lacked quality. Long-time Sunderland servant Sebastian Larsson was especially guilty of giving the ball away cheaply and squandering attacking chances.
The Premier League's bottom side were let off by substitute Kevin Mirallas who slashed wide through on goal. The Belgian had evaded Sunderland skipper John O'Shea but scuffed horribly across goal.
There were more wasted Everton chances at 1-0, Barkley hopelessly fired over on the half volley. He was free after the Mackems failed to clear another Coleman cross, Barkley was off balance as he fired and was no where near scoring.
Despite looking nervous in his first game back Pickford kept Moyes' men in it with 15 minutes left, denying Lukaku. The powerhouse fired across goal with pace after out-muscling Lamine Kone, Pickford showed fast reactions and a strong wrist to deny the marksman.
What followed was pivotal in deciding the contest. Jermain Defoe who had been largely anonymous, was one on one with the back pedaling Coleman, when he let fly. His shot crashed off the bar and bounced away from goal, Joel Robles was completely beaten. The rebound fell to Fabio Borini whose mis-hit cross couldn't pick out an unmarked Larsson waiting to tap home from three yards.
Moments later the game was settled. A fast Everton break saw Lukaku break unopposed from the halfway line, with a clear run on goal, his blocked shot just curled over the sprawling Pickford. At 2-0 a poor offensive team like Sunderland had no chance. Game Over.
Gueye and Valencia could have added to Sunderland's misery. Gueye was denied by an excellent Jones block as he aimed for the corner. Whilst Valencia was through on goal but shot too close to Pickford.
Much like West Brom last month, Sunderland were routinely beaten by top half opposition. Another game has gone in Sunderland's attempts to once again defy the odds and avoid relegation.