It was left to the matchwinner, Olivier Giroud, to say what everyone was thinking. “At home you have to win and even more so after two disappointing results,” said the France forward. “It is a big relief.”

Of all those of an Arsenal persuasion, however, there was no one more relieved than the manager. As the clock ticked towards full-time and the first supporters began to drift away, one dreaded to think how Arsène Wenger would recover from a third game without a victory after the disappointment of successive defeats at Everton and Manchester City.

As he acknowledged, West Brom are not the opponents anyone would pick in such circumstances, given their reputation for dogged resilience, and it looked as though an inspired performance from their goalkeeper, Ben Foster, would be how this game was remembered until Giroud’s late header following an inch-perfect cross from Mesut Özil.

“With 10 minutes to go I thought we could play a draw or maybe, if we were not intelligent, even lose the game,” Wenger said.

“We kept going and in the end, whenwe couldn’t make a difference on the ground, we made it in the air, with maybe the only player in our team who can do that.”

Given the season he has endured, there was a certain irony that it was Giroud who found the breakthrough. Alexis Sánchez has enjoyed such success playing through the middle that this was the Frenchman’s first Premier League start of the season, in the absence of the injured Theo Walcott, and for the majority of the afternoon it was easy to see why as he struggled to make an impact.

He had skied his only opportunity in the first half, then picked up a yellow card and another foul on Claudio Yacob less than three seconds after the restart may have hinted that this was not going to be Giroud’s day.

Yet his perseverance was rewarded in fine style as he won the physical battle with Gareth McAuley to meet Özil’s cross with a looping header that left Foster with no chance.

“He put his hand across him early and outmuscled him,” said the West Brom manager, Tony Pulis, almost in admiration. “I think if Gareth takes a step forward, then he stops Giroud pinninghim. Once he pinned him he is so strong and overpowers him. I’ve got no complaints.”

West Brom have faltered recently, suffering defeats at Chelsea and Manchester United, but they remain a difficult team to break down.

Had Yacob shown more composure when the ball fell to him after Petr Cech’s fumble following a corner midway through the second half, then they could easily have snatched three points against an Arsenal side who looked there for the taking at times. But that escape seemed to spark the hosts into action, with Özil finally waking from his slumber to provide the one moment of real quality that ultimately proved decisive.

As ever, it was not for the want of trying from Sánchez, who could consider himself unlucky to be denied twice by Foster and between times by a post in a matter of minutes after the break.

As it was, Giroud’s goal threatened to open the floodgates and the substitute Aaron Ramsey could easily have added some gloss to the scoreline late on. But any more than a 1-0 victory would have flattered the home team.

“The confidence is swinging and depending highly on the result,” said Wenger. “We have lost two on the trot so of course the confidence has been hit. But it’s a good test for the team. There is no season without disappointment, so it was interesting to see how they responded to disappointment.”

With matches between now and the end of January against Crystal Palace, Bournemouth, Swansea City, Burnley and Watford, there should be optimism that Arsenal’s title challenge may not be over just yet and this was exactly the kind of result that could spark another run of victories.

But Wenger will know his hopes of overhauling a Chelsea side who have won all 12 of their matches since the 3-0 defeat here at the end of September are now out of their hands.

“Maybe, yes,” he replied when asked whether this team is more resilient than it has been in recent years. “It’s normal to say yes but we have to show that for the whole season to maintain that resilience.

“ We are quite a big distance behind Chelsea and we will need a special resilience to come back.

“But I hope that the other teams will have their moments of weakness as well. We can only take advantage if we continue like that.”

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Facebook Twitter Pinterest Alexis Sánchez cut a frustrated figure as Arsenal struggled to break down the West Brom defence. Photograph: Ian Kington/AFP/Getty Images