It was the break that Arsène Wenger and Arsenal needed. Alexis Sánchez’s opening goal was the result of a clear handball, but it helped to earn the win for his team and end the two-game losing streak that had led to the latest outbreak of angst in these parts, and the latest questions about whether Wenger ought to stay on as the manager beyond the summer.

The referee, Mark Clattenburg, felt so bad about his failure to spot the handball on 34 minutes that he said sorry to Hull City’s players.

“When we came out for the second half, the referee’s apologised to us and said there was handball,” Andy Robertson, the full-back, said. “He’s obviously looked at it at half-time and seen he was in the wrong. Not many referees admit they’re wrong, so that’s good, but it doesn’t make it any better.”

Wenger said, with a smile, that “you face a good storm when you lose two games on the trot at Arsenal”, and all he wanted here was the victory, no matter how it came. “It was more about the mathematics than the brilliance today,” he added.

There was an anxious edge to the Arsenal performance; the sense that they were hanging on in the second half – at least until Sánchez scored his second goal from the penalty spot in stoppage time. It was the result of another handball and, this time, it was spotted.

Sánchez had surged forward and taken the ball around Eldin Jakupovic, who had unwisely bolted from his line, before crossing for the substitute, Lucas Pérez. His header was blocked on the line by Sam Clucas with his arm and, to compound the Hull midfielder’s misery, he was sent off.

Arsenal 2-0 Hull City: Premier League – as it happened Read more

Sánchez drilled home the penalty for his 19th goal of the season and Wenger, who was up in the stands as he served the final game of his touchline ban, could exhale.

Hull had played with balance and personality, and they created the chances to have taken something, with Oumar Niasse twice denied by Petr Cech. On this evidence, and that of recent weeks, they have enough about them to stay up. But it did little to soothe the sense of injustice that Marco Silva would speak about afterwards.

The afternoon might have taken a different course had Niasse not been denied by Cech in the 14th minute. There was power behind his header from Kamil Grosicki’s cross and Cech had to be alert to tip the ball over the crossbar.

Moments earlier, Lazar Markovic had robbed Alex Iwobi, surged forward, beaten Laurent Koscielny and crossed the ball low. But it was too far in front of Niasse.

The breakthrough goal should not have stood, but Hull’s protests went unheeded. Sometimes, there is something to be read into the immediate reaction of players in the vicinity of an incident and those of Hull gestured that the ball had gone in off Sánchez’s hand. The TV replays supported them.

Kieran Gibbs’s shot was hacked off the line by Andrew Robertson, after Mesut Özil’s cross had ricocheted off Tom Huddlestone and Sánchez got to the loose ball before Jakupovic. His shot, from point-blank range, was blocked by the goalkeeper, but it looped up, hit Sánchez’s hand, which was raised, and went in.

Özil was strangely hesitant and out of sync, but Arsenal had created the chances to have gone ahead earlier. Héctor Bellerín, who was passed fit after his concussion against Chelsea last Saturday, worked a one-two with Alex Oxlade-Chamberlain only to slice his shot when well placed; Sánchez jinked inside but dragged wide of the post – a bad miss and he knew it; and Özil skied a left-footed volley from Sanchez’s cross. Theo Walcott also had a shot blocked on 32 minutes.

Hull stuck to their game-plan and they refused to be rattled by the unlucky concession. Silva has effected a remarkable uplift since taking over in January and his team’s composure was pronounced. Markovic and Robertson, on the overlap, were dangerous and there were moments when Arsenal were stretched at the back.

Hull threatened an equaliser early in the second half, when Markovic drew in Koscielny before blasting away from him and crossing for Niasse. The striker took a touch on his chest and struck powerfully for goal, only for Cech to beat the ball clear.

Silva’s team could also point to the moment when Gibbs, who was the last Arsenal defender, came across to flatten Markovic as he jumped for a high ball. Hull felt that Markovic had an opportunity to get in on goal, but he did not have the ball under control. Gibbs was booked.

Silva made attacking changes in the second half, introducing Evandro and, later, Adama Diomandé, and – with the full-backs pushing forward and Alfred N’Diaye playing as a box-to-box midfielder – Hull put themselves on the front foot. Sánchez was booked for a dive, but, after Diomandé had headed high from a corner, the Chilean would have the last word.