Charlie Austin gave the hosts an early lead with Arsène Wenger's side left open at the back early on.
Arsenal struggled to break down Southampton but eventually netted with minutes remaining as they moved above rivals Spurs in the race for the top four.
Sloppy start for Arsenal
Arsenal were guilty of making an incredibly slow start against Manchester United last week and against Southampton they were at it again.
Within three minutes the Saints found themselves a goal ahead. Dusan Tadic was able to get away Per Mertesacker before the Serbian played in Austin. The striker was then able to take a touch before firing past Petr Cech for his fourth goal in as many games.
It could have got worse for Arsenal who were making costly errors. Austin almost doubled the lead but Cech was there to make a good save.
The Gunners were then saved by a combination of both offside flag and post as Austin was played in before striking the upright. However he was adjudged to have been in an offside position.
Gunners struggle to break Saints down
Wenger's side dominated possession, but struggled to create many first half chances. Alexandre Lacazette's shot after turning was straight at Fraser Forster before the latter was forced into making a strong save to deny Aaron Ramsey.
Another chance for Lacazette went begging minutes before half time as the Frenchman skied a good opportunity inside the area. However there was a claim for a penalty with Maya Yoshida catching Lacazette late but there were no appeals from any Arsenal player.
Conceding early again made life tough for the Gunners with Southampton happy to sit back through the second half. Because of that the visitors struggled to break their opponents down.
Ramsey looked to add impetus to a frustrating Arsenal attacking display but despite his best efforts could only pull an effort wide after 53 minutes.
Nacho Monreal also tried his luck, curling an effort wide of the target with just over 20 minutes remaining.
Giroud grabs late equaliser
Wenger tried changing the game by bringing Danny Welbeck, Jack Wilshere and Giroud into the fray and it paid dividends.
Alexis Sánchez had a relatively poor game by his high standards but he was on hand to provide an assist that rescued Arsenal a point.
The Chilean curled the ball into the area from the left hand side and Giroud was there to nod home with just minutes to go as things finished all square.