Danny Welbeck thought about it. He had felt the slightest touch from the Milan left-back, Ricardo Rodríguez, inside the area and he went down. The official behind the goal thought about it some more. The seconds ticked by. Milan were unconcerned. But then, a crackle across the airwaves and there was the Swedish referee, Jonas Eriksson, pointing to the spot. Milan erupted with rage. Arsenal could sense their place in the Europa League quarter-finals.

Welbeck scored and, at long last, Arsène Wenger could feel his luck was in. The Arsenal manager’s team had trailed to Hakan Calhanoglu’s long-range blast and, at that point, things could have turned angsty. Instead, Welbeck had them back in charge.

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The impression it was Arsenal’s night was reinforced when Granit Xhaka made the tie safe on 71 minutes. Again, there had been little hint of danger. The midfielder’s shot from outside the area looked routine for Gianluigi Donnarumma. Yet the young hope of Italian goalkeeping fumbled dreadfully and that was that. There was even time for Welbeck to add a late third, after Donnarumma had parried Aaron Ramsey’s header.

Facebook Twitter Pinterest Danny Welbeck nods past the despairing Gianluigi Donnarumma to seal Arsenal’s victory. Photograph: Richard Calver/REX/Shutterstock

There were fears beforehand of another low Emirates Stadium turnout; more refuseniks angry at the club’s direction under Wenger. It did not materialise and there was something fortifying about the sight of a virtual full house roaring the team on. The official attendance of 58,973 looked right, for a change.

Milan came to play and they were understandably aggrieved about the penalty, even if the manager, Rino Gattuso, refused to use it as an “alibi” for the defeat. Arsenal wobbled at the start and they were relieved when the Milan striker André Silva – in yards of space – found only the side-netting after 46 seconds. But Wenger’s team tried to get on to the front foot and they created chances.

This competition has long since come to resemble a shot at salvation for the club and, possibly, Wenger too. The dream of crashing into the Champions League via the back door continues to burn.

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Calhanoglu fashioned his goal out of nothing. He cut across his right-footed shot from 25 yards and got the ball to dip and fade into the far corner. David Ospina was powerless. The fear from the Arsenal point of view was it would prompt a collective panic; a reawakening of the demons that have gripped them all too regularly this season. But as the crowd stayed with them, they responded – with a helping hand from the officials.

When Welbeck went down, Wenger’s words from last month resonated. “I remember there were tremendous cases here when foreign players did it,” he said, with regard to diving. “But English players have learned very quickly and they might be the masters now.” The Italian media put questions to Gattuso about how England had once been considered as the land of fair play. Not here.

Welbeck’s conversion was clinical and Milan would be further incensed moments later when Calum Chambers, who had replaced Laurent Koscielny – the victim of a back injury – felt the ball hit his hand inside the area. No penalty.

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Arsenal were not convincing at the back but they could point to a clutch of chances in the first half. Welbeck put a move on Leonardo Bonucci in the 25th minute before seeing Donnarumma block at the near post; Ramsey worked the goalkeeper immediately after Calhanoglu’s goal and, in first half stoppage time, Welbeck touched back for Henrikh Mkhitaryan, who nodded wide, and Jack Wilshere extended Donnarumma with a decent hit.

Milan’s challenge in the second half was to put the penalty decision behind them, which was hard. The injustice burned. Their supporters had whistled the big-screen replays of Welbeck’s kick during the interval.

Arsenal were eager to draw Milan’s sting with periods of possession but the visitors pushed. They knew that the next goal could re-release the cat among the pigeons. Suso, who would be booked for diving, dragged a shot wide while Patrick Cutrone fluffed a volley when gloriously placed. Silva also went down in the area, looking for a penalty. He might claim that it worked for Welbeck.

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Mkhitaryan and Ramsey had half-chances at the beginning of the second half but it was Milan who came to knock on the door. The substitute, Nikola Kalinic, blew a free header and Wenger was sufficiently worried to introduce Mohamed Elneny as a third man in midfield. Donnarumma’s error, though, would knock the stuffing out of Milan.

Arsenal had done the hard part at San Siro last Thursday, when they turned up and Milan did not but the job still had to be finished. It was possible to feel the stirrings of optimism. The draw on Friday brings possibility.