England midfielder Jack Wilshere started alongside Germany defender Mertesacker, who scored the winning goal against England in a friendly at Wembley midweek.
The Gunners came to life after 15 minutes to camp in their opponent's half. Wilshere almost broke the deadlock with a chipped ball over Boruc that came off the post before Aaron Ramsey hit the same post with a backheeled flick.
But Boruc's lucky day was soon to end as the Saints goalkeeper lost the ball after trying to clumsily dribble past France striker Giroud in his box. Giroud pressured him and easily won the ball before scoring from close range.
"We were a bit lucky on the first goal, but I think that really helped us for the rest of the game," Giroud said. "I didn't give up on my duel with the keeper. Usually I used to go too quickly ... but this time I stand on my legs and was a bit lucky, took ball and scored. It's nice for the team."
Starting the match in 3rd place, Southampton showed a more attacking side to its play after the interval but Adam Lallana saw his powerful attempt at goal stopped by Wojciech Szczesny just before the England midfielder was replaced by Dani Osvaldo.
The Saints enjoyed good spells of possession as Arsenal struggled to win the ball before Mesut Ozil and Santi Cazorla spread confusion in Southampton's box as the match opened up.
Arsenal finally sealed its win four minutes from time after Jose Fonte pulled Mertesacker's shirt.
