West Ham’s bid to become the Premier League’s maverick force is gathering powerful momentum. Any attempt to make sense of their wild inconsistency feels futile at the moment, with the sense of disorder summed up by the sight of Manuel Pellegrini struggling to stifle a laugh as he tried to offer considered analysis on a chaotic performance from his weird and occasionally wonderful side.

Pellegrini is usually much more circumspect when he meets the media. This time, however, he had no option but to chuckle after an afternoon that had featured sloppy concessions, wonder strikes from Felipe Anderson and Robert Snodgrass, a classic piece of poaching from Javier Hernández and a flamboyant comeback that lifted West Ham into the top half for the first time this season.

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“It was a strange game,” Pellegrini said, just as he had after Tuesday’s victory over Cardiff City. His serious face returned and West Ham’s manager switched his focus to how his players had initially found it difficult to recover from James McArthur’s early goal for Crystal Palace. “We played without calm because we were a goal down,” the Chilean added.

West Ham, who have scored three goals in each of their last three matches, certainly appeared to have made the classic mistake of underestimating wounded opponents in the first half. Palace, who lie two points above the bottom three, had a point to prove after letting their supporters down against Brighton in midweek and a determined start brought them a reward in the sixth minute.

Patrick van Aanholt lifted a deep free-kick towards the edge of the area, James Tomkins beat Arthur Masuaku in the air and nobody in claret and blue reacted as McArthur darted in. West Ham’s cries for offside fell on deaf ears, allowing the midfielder to bundle the ball past Lukasz Fabianski.

The London Stadium became an angry, frustrated place. Palace had survived an early scare when pressure from Van Aanholt stopped Hernández from squeezing a shot past Wayne Hennessey, but otherwise the visitors were comfortable.

Facebook Twitter Pinterest Felipe Anderson’s strike flies over Wayne Hennessey for West Ham’s third goal. Photograph: David Klein/Reuters

West Ham’s toothlessness made them pine for the hamstrung Marko Arnautovic and the half ended with Palace almost adding a second. Luka Milivojevic was unfortunate to see his free-kick hit the bar.

Pellegrini responded by reaching for the ultimate Plan B, replacing the ineffective Lucas Pérez with Andy Carroll. West Ham surged forward and quickly equalised out of nothing. Mamadou Sakho’s clearance dropped to Snodgrass, who used his left foot to bend a beautiful shot past Hennessey from 20 yards.

Anarchy reigned all of a sudden. Issa Diop foiled Wilfried Zaha, who will miss Palace’s next match after picking up his fifth booking of the season, and Fabianski denied Max Meyer with a brave stop.

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The next goal felt hard to call. Yet West Ham sensed their moment when Tomkins tripped Carroll in a dangerous position. Anderson whipped the free-kick over the wall, Hennessey failed to push the winger’s effort to safety and Hernández smashed home the rebound.

West Ham went in for the kill. Anderson was in his element now and the Brazilian scored in the 65th minute, curling a stunning shot past Hennessey from the edge of the area.

Anderson’s sixth goal of the season gave West Ham the illusion of safety, prompting them to bring out the flicks and tricks as they moved towards securing three consecutive league wins for the first time since December 2016.

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Such cockiness demanded a reply from Palace, who hauled themselves back when Jeffrey Schlupp, a replacement for the injured Van Aanholt, glanced Meyer’s cross past Fabianski.

Yet an equaliser was beyond Palace. “I don’t know if we collapsed in the second half,” Roy Hodgson said, but his unhappiness was clear. “We did concede three goals.”

What he would give for some of Pellegrini’s attacking options.