Arsenal dominated the match and it was no surprise when, in the 36th minute, Pires broke free on the left to receive a perfect pass from France team mate Thierry Henry and slot home left-footed under the diving body of goalkeeper Antti Niemi.
Southampton looked more like the away team as they tried to contain the north London side, who enjoyed more than 60 percent of the possession. Dennis Bergkamp missed a sitter and Henry and Freddie Ljungberg forced spectacular saves from Niemi.
It was only some desperate defending that kept the scoreline in check.
"It was a deserved victory and a well done job," Arsenal manager Arsene Wenger said, adding hisside might have scored more had Niemi not been in such good form. "In the second half we dropped physically and they got a bit more aggressive," he said.
Southampton won the fixture 3-2 last season with a sizzling performance from James Beattie but on Monday the striker was squeezed out of the game.
Arsenal, unbeaten in the league this season, are now on 45 points from 19 games, three ahead of third-placed Chelsea and 15 in front of the rest of the premier league pack.
Southampton remain in eighth on 26 points. Manager Gordon Strachan said it was the first time he had watched his side playing as though they were frightened of the opposition.
"They must remember that smell of fear," Strachan said of his players' first half performance. "We must remember how we embarrassed ourselves."