It was just as West Ham imagined it when they spent more than £100m last summer. Lucas Paquetá as a false nine. Two left-backs on the pitch at the end. A defence so fragile that Alex Iwobi can score direct from two crosses. The new man in the dugout watching and wondering if life at the London Stadium is always this baffling.

This ended up being a game that West Ham tried very hard not to win, even though they led 2-0 and 3-1 after a host of comical errors from ­Fulham. As it was, all that mattered for ­Graham Potter was taking the points and finding logic in the puzzle.

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Potter has had only three ­training sessions since replacing Julen Lopetegui and, given that he came into his first Premier League game in charge short of forwards, he could afford to look beyond West Ham securing victory by scoring with their only three shots on target.

What a disaster this was for ­Fulham, though. They are winless in the league since beating Chelsea on Boxing Day and lost here because of poor decisions at both ends. West Ham’s goals – scored by Paquetá, Tomas Soucek and Carlos Soler– were all avoidable.

“I’m very happy with the result,” Potter said. “The performance was one of high effort, high togetherness – understanding that we have to suffer at times. It was far from perfect in terms of where we want to be in the long term but as a foundation the players gave everything.”

Potter’s attacking options were ­limited with Niclas Füllkrug, ­Crysencio Summerville, Michail Antonio and Jarrod Bowen missing. He responded by naming a team ­without a recognised striker and it took West Ham a while to adjust. ­Fulham should have led in the sixth minute, only for Harry Wilson to ­volley against the bar.

The visitors were attractive but frustrating. West Ham, who are ­considering a loan move for the RB Leipzig striker André Silva, ­profited when they began to show more aggression after 20 minutes of dominance from Fulham.

Faced with a slightly more urgent press, Andreas Pereira was drawn into playing a blind pass across his own area in the 31st minute. With Bernd Leno out of his goal, Soler ran in from the left to punish Pereira’s carelessness by driving the loose ball into the empty net.

“We are penalised by our mistakes,” Marco Silva, the Fulham manager, said. “It is our fault we lost. We were so dominant until the first goal. We created enough chances to be leading. The best team didn’t win, but we have to be strong at both ends. We gave West Ham two goals.”

Fulham were thrown by Soler’s first goal since joining West Ham on loan. Two minutes later Paquetá, sort of embracing his target-man role, ­disturbed Joachim Andersen in an aerial challenge. The ball broke to Mohammed Kudus and the best move of the half developed, Soler’s chip releasing Aaron Wan‑Bissaka and the right-back pulling the ball back for Soucek to beat Leno with a rising finish.

Suddenly a double pivot of Edson Álvarez and Guido Rodríguez looked quite smart. Soucek, playing as a No 10, had come up with one of his goalscoring runs. Fulham’s response was limited to Raúl Jiménez heading against the woodwork.

The second half brought an improvement from Silva’s team, hope stirring when Antonee ­Robinson ­dispossessed Kudus in the 51st minute. The left-back found Iwobi, whose delivery caused confusion in the West Ham defence. ­Jiménez, seizing on the indecision, did enough without getting a touch to ensure the cross went beyond a distracted Lukasz Fabianski.

Potter responded by introducing Danny Ings for Kudus, who smacked his seat as he took his place on the bench. Soon Silva was watching in disbelief as Leno dawdled in possession, lost the ball to Ings and left Paquetá with another open goal.

Enough? Not when Iwobi made it 3-2, floating another cross past ­Fabianski, nobody in claret and blue taking responsibility. West Ham did not make it easy for themselves. ­Fulham had chances for a point. ­Fabianski denied Jiménez. Sasa Lukic and Adama Traoré were wasteful during added time.

West Ham held on. They are 12th in the Premier League table, two points above Tottenham. This is not ­Potterball yet but it is a start.