The last time Everton were not in the top flight, Winston Churchill was prime minister. Ever-presents among the elite since 1954, they have rarely been in such trouble since. Now, with Manchester United, Leicester, Liverpool and Chelsea next, a club who had Champions League aspirations may soon be found below the dotted line. When Richarlison scored his second penalty, they were set to have a seven-point cushion on Burnley and the bottom three. Instead, a comeback capped by Maxwel Cornet means half an hour effected a six-point swing, leaving Burnley looking rejuvenated and Everton endangered. “If we didn’t know we were in a fight before then we certainly know now,” Frank Lampard said after a harrowing night. He looked browbeaten and beleaguered in the swirling rain at Turf Moor as a wretched record was extended. Everton are yet to pick up a point on the road under him and their sixth successive away defeat may be the costliest yet. Sean Dyche galvanised his team by citing Everton’s sorry statistics, mentioning a meagre haul of six points from a possible 42 away from Goodison Park. “I said it is for us to go and expose that,” he revealed. “I said to the players at half-time: ‘I’m not sure they know how to win a game.’” Neither, arguably, did Burnley, who had won just three of their first 28 matches this season. Now the trip to Norwich on Sunday provides a chance for two victories in five days. Their fortunes certainly changed in front of goal. After scoring three times in 11 games, Burnley scored three in one evening. Indirectly, their manager was a contributor. Dyche showed a golden touch. He recalled Nathan Collins, Jay Rodriguez and Cornet and each scored. The Ivorian also had an assist. So did Matej Vydra, the substitute he sent on as he sought a winner. Dyche had picked an unusually attacking lineup, crowbarring Cornet in on the left wing, and was vindicated. Burnley beat Everton, but once again Everton beat themselves. “We lost points we should have gained,” Lampard said. “The goals are goals we shouldn’t concede. Mistakes are mistakes.” They are far too frequent. Alex Iwobi was culpable for West Ham’s winner at the weekend and was again at fault for Burnley’s opener, failing to track Collins as he volleyed in Cornet’s corner; set-piece problems are a familiar failing. The third was the consequence of two slices: the first from Jordan Pickford, gifting Burnley a throw, the second by Ben Godfrey, finding Vydra. He cut the ball back for Cornet to finish emphatically. “We know Maxwel can score a goal,” said Dyche. Dwight McNeil, who has not scored all season, was dropped. Rodriguez’s goals have also been rarities but his second in 39 league matches was Burnley’s equaliser, the lifelong Burnley fan timing his run into the box to meet Charlie Taylor’s low cross. Cornet’s winner made this the first time Burnley had scored first in a Premier League game, lost their lead and gone on to win. It was proof of character. They recaptured the spirit they lacked against Manchester City on Saturday. Turf Moor has rarely been as raucous recently and Burnley responded. They subjected Everton’s callow defence to heavy pressure. The visitors will have rued the absence of Michael Keane and Allan through suspension, and Burnley’s relentlessness reaped a reward in an entertaining, error-riddled thriller. Their storming finish ensured a remarkable performance by Richarlison was in vain. The Brazilian seemed on a one-man mission to save Everton. He had an overhead kick parried by Nick Pope, clipped the woodwork with a drive and, after Jonjoe Kenny’s cross took flight and struck the far post, almost converted the rebound. He tormented Connor Roberts. He was both brilliant and profligate. He ended a 10-game goal drought by converting two spot‑kicks, the first awarded when Ashley Westwood needlessly tugged Anthony Gordon, the second, after Mike Dean reviewed it on the monitor, when Aaron Lennon caught Vitalii Mykolenko. Both were disputed by Dyche. “The first one is a bundle when he could run and get the ball, the second, my bigger picture is that players have never been more agile, more athletic, more lean, more fit but one tap on the foot and then they are gone.” Lampard had graver concerns. “There are nine games where we have to give absolutely everything, every ounce that we have,” he said. But this was a night when Everton were again rather too generous in their gifts.