The result lifts Everton above Manchester United and into sixth for 24 hours at least while Hull, who had Tom Huddlestone sent off in the second half, stay 18th and are now three points from safety.
Much of the talk before the game surrounded the reception Lukaku would receive from the Everton fans after the striker indicated earlier in the week that he would not sign a new contract.
In the end Lukaku was afforded a rapturous reception from the Toffees supporters, particularly when his two late goals put the seal on a sixth successive home Premier League win.
Everton began the game with purpose and took just nine minutes to open the scoring. Ross Barkley fed a pinpoint pass through to Tom Davies down the right and the midfielder’s low cross was met by Calvert-Lewin for his first goal for Everton.
The same trio nearly combined for a second goal minutes later but Barkley’s searching cross evaded Davies and could not be converted at the far post by Calvert-Lewin
Lukaku thought he had doubled Everton’s lead when he fired low into the corner from Barkely’s pass, but his celebrations were cut short by the offside flag.
Everton then suffered a blow midway through the half when Morgan Schneiderlin pulled up with an injury and had to be replaced by Gareth Barry.
Hull had struggled to create an opening but were almost gifted an equaliser when a mix-up between Joel Robles and Ashley Williams allowed Sam Clucas to nip in but his lobbed shot landed on the roof of the net.
Lukaku had a chance to make it 2-0 early in the second after embarking on a winding run before fizzing a shot just over the bar
Everton boss Ronald Koeman then made a tactical switch, bringing on Ramiro Funes Mori for goalscorer Calvert-Lewin.
Funes Mori nearly made an immediate impact when Eldin Jakupovic could only punch the ball into his path, but the Argentine fired his shot wide of the post.
Jakupovic atoned for that error moments later when he made a superb block from Lukaku’s shot after a raking cross-field pass from Barry.
Hull, buoyed by Everton’s failure to score a second, then began to rally. Omar Elabdellaoui’s dangerous cross found Andrew Robertson unmarked but the defender could only scuff his shot into the side netting.
But just as Hull looked to be rousing themselves for a strong finish they were reduced to 10 men when Huddlestone was dismissed for a lunge on Idrissa Gueye.
That seemed to snuff out any threat from the Tigers and Everton soon made it 2-0 to effectively seal the game.
Substitute Valencia had been on the pitch just over a minute when he played a neat one-two with Lukaku to get in behind the Hull defence and fire home from close range.
Valencia then returned the favour in stoppage-time, feeding the ball through to Lukaku who shot first-time for his 20th league goal of the season.
Minutes later it was four. Elabdellaoui’s poor back pass was intercepted by Lukaku who rounded Jakupovic to complete a resounding victory.