As if struck by a sign from the heavens, Artur Boruc suddenly had a vision: he would, he could, for five seconds only, be Cristiano Ronaldo. The Ballon d'Or was tantalisingly close. Just a stepover here, a Cruyff turn there, and his opponent would be destroyed ... Only in real life, Boruc stumbled and bumbled and Olivier Giroud pounced to score.

It was a barely believable moment. This was more personally punishing than being beaten by a fellow member of the brotherhood of goalkeepers, which happened recently against Stoke.

After that flourish of vaudeville, the tide in this high-tempo contest could not be turned. Arsenal got back to business after the frustration of a bad day at the office at Old Trafford, and increased their lead at the top of the table to four points. "That was vital," Arsène Wenger reflected, on the need to return to winning ways.

"Your character is tested. Can you win straight away again after a big disappointment and the international break? That was really at stake today."

In some ways, the nil was as important as the two as a symbol of Arsenal's case to be a long-term title challenger. In the second half, when Southampton enjoyed plenty of possession and made some dangerous drives towards Wojciech Szczesny's goal, there was a solidity and confidence in the Arsenal back line that contrasted with the moments of panic that have been their undoing in the past. Southampton could be pleased with their effort, especially after a problematic first half, but they seldom found the room to pose serious questions.

Arsenal's probing caused problems even before the opening goal as Jack Wilshere and Aaron Ramsey struck the woodwork with two demonstrations of sublime individual skill.

After Ramsey's fancy flick was diverted by Jose Fonte, Wilshere burst on to the ball and eked out a chip so delicate it sailed over Boruc as if in slow motion. Both teams held their breath to see where the arcing ball would land. To Southampton's relief, it bounced off the base of the far post. Then Ramsey steered a shimmering volleyed backheel against the same section of woodwork. The post to Boruc's right was having a blinder for the visitors.

But there was nothing it could do to prevent Arsenal taking the lead at the third time of asking. With Giroud hovering, Boruc tried to take him on with all the elegance of a pantomime dame wearing the latest in lead-encrusted boots. The Frenchman stole possession and dinked the ball into a vacant net.

Wenger admitted he has at times had words with his own keeper, who has diced with disaster trying to take on strikers in the past, and at half-time he told Szczesny if in doubt, he was welcome to kick the ball at his manager on the touchline.

Mauricio Pochettino was in no mood to dwell on the incident. "Footballers need to be able to learn from these mistakes. Accept it, and move on," he said. "We want to offer 100% support to him."

Boruc's team-mates gave a lot to try to redeem their keeper. They challenged Arsenal with a flurry of set-pieces. Adam Lallana tested Szczesny with a looping shot that needed tipping over. The Arsenal keeper was agile again in beating away Jay Rodriguez's firm effort.

Southampton flew into action after half-time, playing with the zest and determination that has taken them so far up the Premier League table. Arsenal showed the defensive focus, though, to ensure the visitors' efforts were not easily turned into clear chances. A Rickie Lambert shot was blocked, and Rodriguez's lung-busting run halted, before Szczesny was called upon.

Theo Walcott was given a run out for 20 minutes, and the threat posed by his pace meant Arsenal were dangerous on the break. So it was a tall order for Saints to chase without being vulnerable.

In the end a taller order in the shape of Per Mertesacker concluded the result. Fonte tugged the big German back at a corner, and Mark Clattenburg awarded a penalty. Giroud thumped confidently past Boruc to take his tally into double figures. It took him two more months to hit his 10th Arsenal goal last season.

"Other strikers will tell you: 'I am not obsessed with scoring goals,' but if they do not they are sick. He didn't expect it himself to score so many but this will only boost his confidence," said Wenger. The player dedicated the goals to his grandfather, who died on Thursday.

Southampton played well, but paid the price for two critical errors. They want to move on. Arsenal are not in the mood to look over their shoulders.