Romelu Lukaku’s two late goals made him the first Evertonian to reach 20 league goals in over 30 years and lifted his club level on points with Arsenal in the chase for Europa League places.
The Belgian, who this week turned down a contract extension at Goodison, stroked home a routine 15-yard finish in the final minute after Enner Valencia’s through ball played him beyond the Hull back line to make it 3-0 with his 20th league goal.
And deep in injury-time, a terrible back pass from Ahmed Elmohamady was steered directly into the path of Lukaku who rounded the keeper and claimed his 21st - the first Evertonian to hit that many league goals since Gary Lineker’s 30 in 1985-86.
Earlier, however, Lukaku’s prodigious scoring feats had taken a back seat, as goals from youngster Dominic Calvert-Lewin and Inner Valencia ensured Everton continued form which has seen them collect more league points in 2017 than any other team.
Calvert-Lewin, who turned 20 on Thursday, took just eight minutes of his first Premier League start to claim his first Premier League goal with a move that demonstrated just how tall a task it will be for the Hull manager Marco Silva to keep his team in the top division.
The impressive Ross Barkley played a superb pass inside a defender for Tom Davies to chase and his low cross into the six-yard area found Calvert-Lewin having slipped his marker and able to convert from six yards.
Hull remained in contention until the 72nd minute when their key midfielder Tom Huddlestone was harshly shown a straight red card by referee Paul Tierney for a foul on Idrissa Gueye.
And six minutes later, Everton finally found the second goal they had sorely needed, through substitute Valencia, who played a clever one-two with Lukaku on the edge of the area, controlling the return on his chest and calmly slotting home from six yards, a goal which doubled the early lead handed them by Calvert-Lewin.
A £1.5 million signing from Sheffield United last summer, the forward was playing on loan for non league Stalybridge Celtic two years ago but certainly did not look out of place in more illustrious surroundings, an indication of how well manager Ronald Koeman has handled his development.
The timing of the goal also ensured that Hull, quietly solid and impressive enough in defeating Swansea seven days earlier, were left with a mountain to climb.
Astonishingly, they could, probably should, have gone in level at the interval after Ashley Williams’ under-hit back header to goalkeeper Joel Robles on 38 minutes was intercepted by Sam Clucas who could only hurry a chip over the cross-bar.
Had Everton conceded, they would only have had themselves to blame for having not already wrapped up a sixth consecutive home victory.
All eyes were on Lukaku who, it should be said, encountered no negative treatment from home supporters despite the news this week that he has rejected a contract extension at Goodison, but the forward was strangely quiet in the first half.
He was involved in setting up a chance for Seamus Coleman, however, with the defender drawing a good save from Eldin Jakupovic.
Barkley’s dangerous low cross just eluded both Davies and Calvert-Lewin on the six-yard line as they tried to make contact and, late in the first half, Davies’ excellent through ball seemed to have played in Barkley only for the England international’s control to let him down.
The loss of Morgan Schneiderlin, to injury after half an hour, did not help Everton’s rhythm and they struggled to re-establish their superiority as the second half began, especially when Hull won early corners.
But Barkley soon set up a chance for Lukaku on the break, with the Belgian advancing menacingly to the edge of the Hull area before shooting narrowly over.
And, just before the hour, Jakupovic flapped horribly in trying to punch away a Leighton Baines cross and substitute Ramiro Funes Mori, on for goalscorer Calvert-Lewin, placed the rebound inches wide.
Lukaku, seeking his 20th league goal of the season, looked in the mood to claim it as soon as possible, collecting a magnificent cross-field pass from Baines in his stride, and delivering an equally impressive shot which Jakupovic did well in parrying away.
Andy Robertson reminded Everton that Hull still posed a threat, volleying into the side netting from eight yards, although the sending off of Huddlestone soon afterwards was clearly not what the visitors needed.
“Did that surprise you?” said Koeman of Lukaku. “He’s a professional and every professional gives their best for the club, for the players, for everybody.
“It was difficult for Rom but when he got more space - and we need to understand it was 11 against 10 - then he played well. When he gets those kind of chances to score, then he will score.
"The fans love Rom and everyone loves Rom. Yes, you may be able to hold him back for 85 minutes but then he was focused to the last second. We killed the game perfectly.
"You need to have hope in life! Of course we like to keep best players and we will do the maximum to keep these players but the final deciwsiomn will be with the player himself.
“That’s sometimes strange in football. It wasn’t our best home performance and it was a lot tougher than the final result.”
Huddlestone was shown a straight red by referee Paul Tierney for a challenge on Idrissa Gueye which was certainly deserving of yellow but probably little more.
“It was harsh, too harsh,” said Koeman. “It’s a yellow, not a red. But okay …”
Opposite number Marco Silva said: “The first 25 minutes of the second half we controlled the game,” said the Hull manager. “We caused problems for Everton and Ronald brought on another centre-back.
“So we didn’t deserve the situation. It left us with big problems, playing with 10 men. There is only a moment for the referee (to make the decision) but we didn’t deserve it.”