Everton extended Abdoulaye Doucouré’s contract on Wednesday and the midfielder repaid them by extending their residence in the top flight of English football into a 70th year. On a day of exhausting emotion at Goodison Park – “a horrible day”, Sean Dyche admitted – the midfielder struck a superb, critical winner against Bournemouth to ensure Everton avoided a first relegation since 1951. There was a nerve-racking finish where 10 minutes of added time, an injury to Jordan Pickford’s hand and the determination of Gary O’Neil’s team to prove they were not on the beach made Everton fight to the last for their Premier League status. When it was finally over, Doucouré had etched his name alongside Barry Horne, Graham Stuart and Gareth Farrelly as Everton last-day saviours. Dyche had completed the impressive achievement of keeping afloat an imbalanced squad that had spent the majority of the campaign without a proven goalscorer. And, as the fans and Dyche himself made clear afterwards, the time has come for seismic change at Everton or these desperate scenes will be back again. There are only so many times you can play with fire without getting burned. The final whistle sparked a pitch invasion that the PA announcer had warned against before and during the game, but it was nothing like the outpouring of joy that greeted last year’s escape against Crystal Palace on the penultimate game. This time Goodison reverberated to chants of “Sack the board” as fans again made their feelings clear over the appalling mismanagement of Everton under the ownership of Farhad Moshiri and stewardship of the chairman, Bill Kenwright. Dyche captured the mood perfectly in his post-match press conference when warning there are no quick fixes at Everton and a change in culture was needed at a club that have not acted big for some considerable time. He has had to contend with an array of issues since replacing Frank Lampard in January and his team selection for the final day was a reflection of Everton’s poor recruitment strategy over several years. A five-man defence for a must-win fixture appeared a negative move from the manager but he had little alternative. With every recognised full-back out injured, Dyche deployed Dwight McNeil and James Garner as makeshift wing-backs. The pair were immense. With no decent striker available because of Dominic Calvert-Lewin’s latest hamstring problem it fell to Demarai Gray to lead the attack. He ran himself into the ground. The paucity of Everton’s options was further demonstrated by their bench. Dyche was unable to name a full complement of nine substitutes even with two goalkeepers among them. Roared on by a passionate Goodison crowd the home side enjoyed periods of healthy pressure in the first half but clearcut openings were limited. There was also little evidence of Bournemouth’s well-documented frailty at set pieces as the visitors stood firm against the aerial threat of Yerry Mina, James Tarkowski and the recalled Conor Coady. Bournemouth were without Neto, their first-choice goalkeeper and captain, after he flew home to Brazil on Saturday as a result of the death of his mother. His teammates wore black armbands in tribute – as did Dyche – and his place went to Mark Travers, the Republic of Ireland international who played in Bournemouth’s Carabao Cup and Premier League wins over Everton earlier in the season. Travers enjoyed the upper hand once again in the first half with fine saves to deny Idrissa Gana Gueye and Garner. O’Neil’s team carried a threat whenever they countered, particularly down their right flank where David Brooks and Adam Smith looked to double-up on McNeil. Marcos Senesi was close to putting Bournemouth ahead when, from a corner that Brooks sliced back into the penalty area, his daisy-cutter rolled through the legs of Mina and trickled wide of the far post. Dominic Solanke was also presented with a good chance when Brooks dispossessed Tarkowski just outside the Everton box. Mina spared his defensive colleague with a vital touch on the former Liverpool striker’s shot. With Leicester beating West Ham, Everton had to win to avoid the drop. The precious breakthrough arrived early in the second half when a patient home move ended with Gueye sending a searching cross towards Amadou Onana. Brooks won the aerial challenge but his header dropped to Doucouré, unmarked on the edge of the Bournemouth area, and the midfielder connected with the sweetest half-volley that flew inside Travers’ left hand post. There was pandemonium and a deafening sound inside the stadium. Doucouré was almost in tears. A goal that should have brought relief ignited anxiety instead – in the Everton performance and home crowd. Kieffer Moore, on as a substitute, spread panic through the Everton ranks with his aerial prowess and one downward header almost set up Solanke. Coady intervened superbly, before Solanke pulled down Pickford and sparked a melee that the striker claimed involved a bite from Mina. TV replays were inconclusive. “Dom hasn’t mentioned that he was bitten,” said the Bournemouth manager. “I’m sure if he was it will be looked at and something will be done about it. I’m proud of our performance today. People might have questioned our motivation but we gave everything to win for 100 minutes.” In stoppage time, with Everton fans chewing through their nails, Pickford produced a vital save to prevent Matías Viña volleying a Moore header into the bottom corner. It got to the stage where Everton were cheering throw-ins in the final seconds. And then they were safe. Just. The time for a huge reset at Goodison is long overdue, but it has to start now.