It was only a point but, considering the manner in which it was achieved, felt like so much more for Bournemouth, and it would not be beyond the imagination to suggest this could be a turning point in their first top-flight season. They were two goals down with 10 minutes to play, level five minutes into stoppage time but somehow fell behind and levelled again in the most dramatic of conclusions.

First-half goals from Funes Ramiro Mori and Romelu Lukaku, his eighth in eight games, had Everton firmly in control but Eddie Howe’s team, displaying a wonderful never-say-die attitude, fought their way back to 2-2 thanks to efforts from Adam Smith and Junior Stanislas in the final 10 minutes.

Yet they almost threw it away again when Ross Barkley’s goal deep in time added looked like ensuring a third win from four for Roberto Martínez’s side, the midfielder’s low finish scrambling past the substitute goalkeeper Ryan Allsop. Everton’s fans invaded the pitch to celebrate, leading to the referee Kevin Friend adding on additional time to the five minutes advertised, and when play restarted Stanislas headed a Charlie Daniels cross from the left home.

Cue wild scenes of jubilation around the rest of this small but electric ground. While they remain two points from safety, Bournemouth’s players departed with a newfound sense of belief. Dauntingly Chelsea, Manchester United and Arsenal will be faced in December, but moments like these can be defining. “I couldn’t believe it,” Howe said. “I am very proud of the fightback from our lads, it shows the character of this squad.”

Everton were a level above in the first half and Funes Mori’s opening goal had been on the cards. Adam Federici, who needed treatment early on after landing awkwardly when punching clear a corner and was eventually replaced at half-time, denied Arouna Koné and Lukaku while also getting in the way of a tame James McCarthy attempt.

There was, however, little he could do to deny the Argentinian defender his first goal for Everton and the team’s first from a set piece this season. Barkley sent in a deep corner and after climbing higher than Steve Cook, the centre-half directed a header across goal, far from the keeper’s reach. Joshua King could not clear it off the line.

Questions must be raised over the hosts’ defending for Lukaku’s simple second, though plenty of credit should go to Gerard Deulofeu for sending a delicious pass from the right into the Belgium striker’s path. The ease with which Lukaku turned Cook before burying the ball past Federici at the near post left Howe shaking his head in disgust.

Cook was hooked at the break, and the club’s third-choice keeper, Allsop, who spent last season on loan at Coventry, made his top-flight bow after Federici was deemed unfit to continue. Howe’s initial diagnosis was that it is a serious ankle injury.

There were encouraging signs on the restart. King pick-pocketed a dozing Barkley before his attempt was blocked by John Stones, Dan Gosling headed a Daniels cross into the arms of Tim Howard and the left-back also forced the Everton keeper to save.

Lukaku was denied a second by Allsop after Seamus Coleman delivered a tasty cross from the right but Bournemouth’s pressure continued to build, their belief never wavering. And with 10 minutes to go a lifeline arrived as Smith halved the deficit with a sublime long-range effort that went in off a post after Everton failed to clear a corner and the substitute defender was left unmarked outside the area.

Everton looked out on their feet and with the division’s smallest stadium suddenly vibrating Bournemouth threw everything forward. King danced down the right before sending a low cross in and Stanislas was on hand to slot home first time at the near post past Howard.

There were three minutes left but it all seemed like an appetiser to an incredible finale. Fed by Coleman, Barkley’s goal from eight yards looked like being enough, but with 97 minutes and 13 seconds played Stanislas arrived to head home Daniels’ cross from a similar distance. “At times in football you have to accept these moments,” Martínez said. “We lost two points twice – that’s a feeling that’s difficult to explain.”