Kingston upon Hull - Everton's mercurial talent Ross Barkley's header secured them a 2-2 draw with struggling Hull in their Premier League clash on Friday.
Barkley, who has lost his place in the England squad and been in and out of the Everton first team under manager Ronald Koeman, allowed the visitors to level for the second time.
Hull skipper Michael Dawson and then Robert Snodgrass, with his eighth of the season, had given Hull the lead on two occasions.
An own goal by Hull 'keeper David Marshall at the end of the first-half had gifted Everton their first equaliser.
The point sees Hull, who have not won in their last eight, climb off the bottom and go a point ahead of managerless Swansea who play later this weekend.
"I think it's a terrific point," said Hull manager Mike Phelan, who has the daunting prospect of seven games in January with a limited squad.
"The goal we conceded at the end of the first half changes your whole way of thinking.
"We are in a battle for the rest of the season but we're up for it."
Everton, with just two wins in their last nine games, remain marooned in seventh spot, six points adrift of Manchester United.
Koeman, who will look to strengthen the squad in the January transfer window, was not too despondent about the end result.
"I think the crowd loved this game because it was really open," the Dutchman told Sky Sports.
"Twice we showed great character and a good reaction.
"We fought for everything. We had the better chances to win the game. You like to win every game, but sometimes you have to be happy with one point."
Dawson pounced with a lovely strike for his third goal of the season although Everton would look askance at veterans Phil Jagielka and Gareth Barry.
Jagielka was beaten to a header at the near post by Curtis Davies while Barry reacted too slowly when the ball fell to Dawson.
Everton awoke to give Hull a few scares, Kevin Mirallas's deflected shot being scrambled away for a corner by Marshall and a superb Barry cross being headed against the post by Seamus Coleman.
Barry, belying his 35 years, was at the heart of most of Everton's attacking play and he went close himself from long range.
Hull, though, looked to be set to go in to the break with a rare lead until Marshall's awful blunder instead gave Everton the psychological advantage as they levelled with the last action of the half.
Marshall had his hands warmed early in the second-half but this time he made a sharp save from Romelu Lukaku's deflected effort, tipping it onto the bar.
Hull went agonisingly close to regaining the lead in the 55th minute as leading scorer Snodgrass' superb freekick beat Joel Robles in the Everton goal but was denied by the post.
Robles, who has earned a run in the team with the injury to Maarten Stekelenburg, did well to prevent Dawson doubling his tally on the hour mark when the centreback was found by Egyptian Ahmed Elmohamady.
However, there was nothing Robles could do with Snodgrass's second superb freekick.
It was awarded after Leighton Baines had fouled the impressive Harry Maguire who had seized on an error by Idrissa Gueye and run deep into Everton territory.
Hull were edging towards an invaluable victory when Barkley struck, heading home from Baines's pinpoint cross.
Everton could have stolen all three points in the final minute of normal time as Coleman's superb cross was met by substitute Dominic Calvert-Lewin but his header flashed wide of the post.