A single point was not nearly enough for Bournemouth. The wear and tear on a talented but brittle squad has enveloped European ambitions. The previous Champions League hopefuls, turned Europa League hopefuls now, turned Conference League hopefuls have not won in 90 minutes in eight matches and in east London almost fell victim to a dozing opponent belatedly realising they were playing for their lives.

The West Ham manager, Graham Potter, had lately suggested the players he inherited in January are now playing for their futures. A winless run since 27 February has sharpened his axe. Relegation might have been averted but the Hammers are on course for what would be their joint-worst season since they went down in 2010-11, so a decisive summer awaits.

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Potter has a more ruthless, sharper edge than his calm public persona might suggest. A dreadful first half from his team was followed by a marked improvement in which changes by their unimpressed manager brought about a revival. Forgotten summer signing Niclas Füllkrug’s header lifted a cat-napping London Stadium, attentions switched away from the conclusions of the Grand National, and when Jarrod Bowen scored an equally good header, Bournemouth appeared sorry and sunk only for Evanilson’s second to rescue a point.

Whether Lucas Paquetá is part of future plans almost certainly depends on the verdict of an independent FA panel on four counts of spot-fixing. The Brazilian, a player vital to club and his country, is playing under a shadow that is likely to lift or descend in the coming days. If this was farewell, he signed off with a forgettable performance.

Bournemouth might have been ahead in the opening seconds when Evanilson nodded wide Dango Ouattara’s cross. The Burkinese winger’s battle with Aaron Wan-Bissaka was a rare highlight among drab beginnings, where the main talking points were usually tracksuited Potter’s wearing of a suit but no tie, and Caledonian cult hero Andy Irving being the cover star of the match-day programme but not named in the match-day squad.

With Füllkrug on the bench alongside Evan Ferguson, neither yet convincing in a Hammers shirt, it was left to Bowen to lead the line. Bowen, the club captain, had not scored or assisted at the London Stadium in his past five games, furthering the idea he is more effective down the flanks than through the centre.

Jarrod Bowen heads West Ham in front in the 68th minute. Photograph: John Walton/PA

Perhaps that was the reasoning behind Tomas Soucek initially playing so close to Bowen, in what time-honoured Hammers may recognise as the Teddy Sheringham role, though in the first half the Czech came closer to scoring at the wrong end when the ball bounced from his midriff and Alphonse Areola was forced to save.

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The keeper was less convincing when palming Antoine Semenyo’s effort into Evanilson’s path for the opener, the Brazilian scoring his fifth in six. VAR briefly intervened, on the last weekend before semi-automated offsides come into play, but Evanilson was level with Maximilian Kilman. Illia Zabarnyi nodded against the bar seconds later, as Bournemouth moved up a gear against opponents who appeared to be running through holiday brochures in their mind’s eye.

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After swapping Emerson for Ollie Scarles at the break, Potter waited ten minutes to throw on Füllkrug and Carlos Soler, the Soucek experiment abandoned. The Hammers were staring down the barrel of seven homes games without scoring before the German took seven minutes to nod in his first ever London Stadium goal, the type of crashing header with which he made his reputation, from James Ward-Prowse’s inviting corner.

Soler went close soon after. Potter has always been an adept in-game manager, the doubts have usually come about his starting selection, and the same will be true of that dreadful first half. In taking the lead, coming in from his rightful flank, Bowen scored a headed goal Füllkrug would have been proud of.

It was Bournemouth’s turn to wake from their torpor. Evanilson tapped in Dean Huijsen’s towering header, and the chase for a winner oscillated from end to end, Semenyo went close. Bowen dragged over when in his favourite inside-left shooting position. Summer and the beaches now beckon for both teams. When the final whistle came, a number of Bournemouth players sank to the turf. They may have not much more to give.