Sam Allardyce talked his way into trouble during his ill-fated spell as England manager. He may not be talking his way out of it during an increasingly unhappy time at Everton. After a sixth successive away defeat prompted the travelling Evertonians to turn on him for the first time, Allardyce claimed: “I feel worse than the fans.” He had the self-awareness to add “they won’t believe this” and, given the level of discontent, that seems a safe assertion; they won’t. The supporters had told him in no uncertain terms where to go when he substituted the goalscorer Cenk Tosun. Further vitriolic dissent followed the removal of the excellent Gylfi Sigurdsson.

If there is a crisis of leadership at Goodison Park, Ashley Williams contributed. Allardyce’s chosen captain was sent off for elbowing Ashley Barnes. “Silly,” said his manager, who will fine the defender. “It sums up our day.” Once again, Everton contrived to undermine themselves but while Allardyce was offered ample indications their supporters want him consigned to the past, Burnley made a minor piece of history. Sean Dyche’s side had not tasted victory since the heady December night when they went fourth. This was the first time since 2010 they have won a Premier League game where they conceded first, a 53-game run ended by a combination of spirit, directness and managerial intervention. Dyche brought on Chris Wood for the ineffective Jeff Hendrick at the break and Burnley’s record signing justified the switch to 4-4-2 by heading in the winner. “I thought it worked,” said Dyche.

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In the process, Burnley beat their past. Michael Keane’s return to Turf Moor felt traumatic. Burnley pocketed £30m for his services last summer. Barnes escaped from his former team-mate to score the leveller. Wood outjumped the man whose sale helped finance his arrival for the decider. Nor did Keane’s centre-back sidekick fare any better. Williams was the first to lose Wood when Johann Berg Gudmundsson centred. “We decide not to defend a corner properly,” said Allardyce.

Under other circumstances, he may have been congratulating himself on his decision-making, even if that still felt illogical. Rewind to the comparatively balmy days of early February and he suggested Tosun was struggling with the English weather. Brought in from the cold, but into the cold, the £27m striker opened his Everton account in an accomplished display to render it a mystery that he had not started for six weeks. “He worked extremely hard,” said Allardyce, who said the Turkey international’s unpopular departure came because he was tiring.

Tosun’s graft had been allied with craft, a lovely curling pass bringing a chance for Theo Walcott. His goal had shown predatory expertise and the sort of aerial ability Allardyce tends to appreciate in a striker. Tosun headed in when the returning Séamus Coleman flicked on Walcott’s cross.

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“We lost it by not scoring the second goal,” Allardyce said. Walcott was the major culprit, but Sigurdsson was the creator in chief of a series of openings. He was incisive, inventive and influential, illustrating what he could do when Wayne Rooney was benched.

Yet Everton faded. “To see the players underperform in the second half is very disappointing,” Allardyce added. The one exception was Jordan Pickford, who pressed his case to be England’s World Cup goalkeeper in front of the watching Gareth Southgate. He amounted to a one-man resistance, making two terrific saves from Barnes, thwarting Ben Mee and denying Aaron Lennon a goal against his old employers.

But Burnley were relentless. Matthew Lowton created three wonderful chances and a through ball was weighted and curled perfectly for the onrushing Barnes to level. “As good a pass as you will see,” said Dyche. It led to a first win in 13 attempts. “Facts are facts,” the Burnley manager added. “It’s been a tough run.” Now, however, Burnley should be safe. “It is a big marker to get to 40 [points] with nine games to go,” Dyche added. Burnley’s future seems secure, Allardyce’s rather less so.