Swansea City have been a bogey team for Arsenal at the Emirates Stadium. On six previous Premier League visits, they had won three and drawn one and, when Sam Clucas put them in front, it was possible to fear that a long afternoon lay ahead for Arsène Wenger and his players.

The nerves jangled among the home support during the first half and but for a one-on-one block from Petr Cech that denied Jordan Ayew in the 45th minute Swansea would have been two goals to the good at the break. “At half-time, I could be worried because we were 1-0 down and I knew that Swansea had conceded only one away goal the whole season,” Wenger said.

Cech’s save would prove to be the decisive moment because Arsenal were a team transformed in the second half. Inspired by Sead Kolasinac – a rampaging presence on the left – they turned things around to win with a measure of comfort. The Swansea hoodoo would not strike on this occasion.

Wenger had described his club’s home form as “impeccable” and it is now eight wins out of eight in all competitions this season – five of them coming in the Premier League.

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Kolasinac scored the equaliser with a bullet of a drive before he got the assist for Aaron Ramsey’s winner. The only disappointment was that he was forced off on 78 minutes with a recurrence of a hip problem. Wenger made it sound as though Kolasinac had to be a doubt for next Sunday’s trip to Manchester City. After a weekend off for the international break, Arsenal host Tottenham.

Wenger’s team hogged 73% of the possession and they had 17 shots to Swansea’s four but the statistics did not tell the story. Swansea executed Paul Clement’s game plan to perfection in the first half and they will look back upon Ayew’s chance with regret.

The striker robbed the dawdling Per Mertesacker inside the Arsenal area and, suddenly, he had only Cech to beat. The goalkeeper made himself big to save. “If that goes in, it’s a totally different situation,” Clement said. “These are the fine margins we are dealing with.”

Swansea had arrived with a question mark at left-back. Martin Olsson, the club’s only specialist in the position, was out with hamstring trouble and so Clement asked Clucas to fill in at left wing-back for the first time since his £16.5m summer move from Hull City. The move would enjoy a stunning dividend.

Swansea had barely crossed halfway in the game’s opening quarter but when Laurent Koscielny took a heavy touch and then slipped over, Tammy Abraham slid Clucas in behind Héctor Bellerín. He finished low and left-footed beyond Cech for his first goal in Swansea colours.

The visitors had previously conceded only once in four away league games this season and it was plain that Arsenal had it all to do. Their big moment of the first half came in the 41st minute when Kolasinac fed Alexis Sánchez and he extended Lukasz Fabianski, the former Arsenal goalkeeper, with a right-footed shot.

That apart, the pickings were slim. Wenger described the opening 45 minutes as “laboured” which was putting it mildly, and his team was booed off at the interval. Whatever he said during the break, it had the desired effect.

Wenger sent his players out early for the second half and they found their stride straight away. Kolasinac’s goal came after Alexandre Lacazette had dug out a smart backheel on the right of the area and Mesut Özil smuggled the ball on.

The Bosnian had a long run at the breaking ball and he thumped it into the far corner. The impressive Abraham had the ball in the net immediately afterwards only to be pulled back for offside but Arsenal could feel that the shackles had loosened.

Koscielny fluffed a free header from a Sánchez free-kick before Kolasinac teed up Ramsey. Not for the first time, Granit Xhaka spread the play with a raking pass and Kolasinac put plenty of pace into his cutback, which Ramsey harnessed with his first-time shot.

The Emirates could relax and so could Wenger on the occasion of his 800th Premier League game.

Ramsey shot high, Lacazette worked Fabianski, Bellerín hooked a shot against the crossbar and the substitute Olivier Giroud, winner of Fifa’s best goal award on Monday, twice went close. Swansea, who are out of the bottom three only on goal difference, did not threaten the equaliser.