At the final whistle, both teams struggled to make sense of their emotions.

They had taken part in a contest that defied logical analysis, with Richarlison’s brainless red card summing up the chaos, and the only thing that felt predictable in the end was Bournemouth reminding everyone why they deserve to be regarded as the Premier League’s escape artists.

Eddie Howe’s side have earned 20 points from losing positions in 2018 and they pulled off their latest high-wire act in challenging circumstances, fighting back from two goals down against Everton thanks to a late flurry from Josh King and Nathan Aké. Yet for all that he praised his team’s ability to cope with adversity, Howe could not be entirely pleased with how an afternoon of relentless drama unfolded. “The frustration is letting it get to that position,” Bournemouth’s manager said. “With the numerical advantage, you expected us to come out and pin Everton in. That never happened.”

Howe knew that he should have been celebrating a third consecutive win, not breathing a sigh of relief at snatching a spirited point. Everton, after all, were there for the taking after losing Richarlison for a butt on Adam Smith in the 41st minute. Yet the visitors rallied in the second half and Bournemouth seemed to be heading for an avoidable defeat after Smith received his marching orders for a foul on Theo Walcott.

“We had a fantastic first 25 minutes of the second half and we really believed when we had the ball,” Marco Silva said. “We scored two fantastic goals. At 2-0, though, we had to keep the balance.”

Everton could not shut up shop. They allowed the game to remain ragged after taking control with goals from Walcott and Michael Keane, who was said to be in an improved condition after being taken to hospital after a late clash of heads with Idrissa Gueye, and Silva had to be content with his new side maintaining their unbeaten start to the season.

Silva was unhappy with a point, although the Portuguese had to accept that Bournemouth were the better side for much of the first half. They set a brisk pace and ought to have taken the lead in the 15th minute, only for Callum Wilson to blaze over from 12 yards after a perceptive assist from Ryan Fraser.

Four minutes before the interval, Richarlison let his teammates down with an act of breathtaking stupidity. One moment Leighton Baines was about to take a throw deep on the left, the next the fans behind Bournemouth’s goal were up in arms. Richarlison had turned to bicker with Smith and, when the pair advanced on each other, Everton’s £40m winger made an aggressive movement with his head, leaving Lee Probert with no option but to send him off.

“It’s something I don’t like to see,” Silva said. “You see it many times.

“Maybe there was minimal contact but he did it. If you are 18 or 19 or 33 you have to keep your balance, even if you are provoked.”

Everton no longer had the Brazilian’s pace as an outlet and Silva changed his team’s shape at half-time, moving Gylfi Sigurdsson to left midfield.

Yet they had coped in similar circumstances two weeks ago, drawing at Wolves after losing Phil Jagielka to a red card, and they went ahead in the 56th minute. Cenk Tosun’s pass caught out Bournemouth’s high line and Walcott sprinted away from Aké before firing past Asmir Begovic.

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That was the cue for a Bournemouth implosion. Five minutes later, Jordan Pickford’s long clearance bounced all the way through and the Everton fans chortled at Smith, who was the last man back, seeing red for clipping Walcott’s heels. “I think it’s a foul,” Howe said. “I think he’s just brushed Theo. The referee just has to make a decision about whether it’s red or yellow.”

Walcott’s speed unsettled Bournemouth and it was his quick thinking that led to Everton’s second goal in the 66th minute. He tapped a free-kick to Sigurdsson on the right and Keane met the Icelandic midfielder’s cross with a firm header.

However, Bournemouth earned a penalty when Baines bundled into Wilson in the 75th minute. King snuck the ball past Pickford and Howe’s men were level four minutes later, Wilson heading against the right post and Aké gobbling up the rebound. Everton, who have loaned Yannick Bolasie to Aston Villa, could only reflect that this was the Premier League in all its eccentric glory.