Romelu Lukaku struck a stoppage-time brace to add to earlier goals from Dominic Calvert-Lewin and Enner Valencia as the Toffees maintained their 100% home record in the Premier League since the turn of the year.
It looked like being a mismatch even before the game began, with Everton now having only lost one of their last 18 Premier League home games and Hull without a win on the road in 14 league games since August, and it took the Toffees just nine minutes to set the contest on the predicted course.
Much of the build-up to the match had surrounded Lukaku's decision to reject a club-record contract from Everton, but the Belgian shrugged off the speculation over his future and had the ball in the back of the net midway through the half, only to be denied by the offside flag.
There was a blow for the Toffees on the half-hour mark as Morgan Schneiderlin was forced off injured, being replaced by Gareth Barry, but Everton continued to control the game and were close to a second 10 minutes after the interval when Lukaku fired narrowly over on the counter-attack.
An error from Eldin Jakupovic handed Everton another chance moments later, but Barkley could only put his shot wide of the target before the hosts saw another opening blocked shortly afterwards.
It seemed like a matter of when the second goal would arrive rather than if it would, though, and Jakupovic was called into action again shortly after the hour mark when Lukaku lashed a curling effort on target.
Hull were looking for back-to-back wins for the first time since August following their valuable 2-1 victory over Swansea City last weekend, but Oumar Niasse - who scored both goals in that match - was ineligible to play against his parent club and the Tigers struggled to threaten at all in his absence.
The visitors' hopes of getting back into the game were dealt another blow with just over 15 minutes remaining when captain Tom Huddlestone was shown a straight red card for an over-the-ball challenge on Idrissa Gueye.
It took just five minutes for Everton to make their numerical advantage pay as Valencia - who had only been introduced as a sub 69 seconds before - exchanged passes with Lukaku before firing a finish past Jakupovic.
Those roles were reversed in the first minute of stoppage time as Lukaku got in on the act, latching on to Valencia's incisive through-ball before sweeping his finish past the keeper to put him out on his own as the Premier League's leading goalscorer this season.
It was the Belgian's 20th goal of the campaign, becoming the first Everton player to reach that tally in a single league season since Gary Lineker 21 years ago, while it also took him to 80 Premier League goals overall, becoming only the third player - after Michael Owen, Wayne Rooney and Robbie Fowler - to reach that tally before their 24th birthday.
Lukaku was not done there, though, and the striker reiterated his importance to Everton with a second late on as he pounced on a loose back-pass before rounding the keeper and stroking his finish into the empty net.
Everton have now won six consecutive home league games for the first time since April 2014 to lift them one point above Manchester United in sixth, although the Red Devils do have three games in hand over Ronald Koeman's side.
Hull, meanwhile, remain 18th in the Premier League table but now find themselves four points from safety following Crystal Palace's 1-0 win over Watford.