Charlie Austin's early opener appeared to have been enough for the Saints until Giroud marked his appearance from the bench with yet another important goal in a Gunners shirt.
Despite sharing the spoils, both clubs make headway in the standings with Arsenal now sitting in fifth place and Southampton moving into the top half of the table.
Saints boss Mauricio Pellegrino opted to start the game with a 4-4-2 formation and it had an immediate effect as the home team took the lead with barely 120 seconds on the clock.
After Dusan Tadic had broken behind the Arsenal midfield, he played the ball through to Austin who kept his composure to flick the ball past the advancing Petr Cech from 12 yards out for his fourth goal in four matches.
Moments later, Austin should have added a second when breaking clear down the right-hand side of the pitch but after moving into the penalty area, the forward drilled his low strike too close to Cech.
Forster also had to be alert to keep out a first-time strike from Aaron Ramsey inside the penalty area, with the England international saving well down to his left.
For all of their pressure, Southampton came closest to a second when Granit Xhaka almost put through his own net from close range, but the home side were full value for the lead at the break.
Arsenal wasted no time in going on the front foot at the start of the second half but it was Southampton who created the first opportunity with Nathan Redmond seeing a 25-yard effort comfortably saved by Cech.
The Gunners were dominating possession but Southampton twice went close to doubling their advantage just after the hour mark, with Oriol Romeu first trying his luck from distance and hitting the top of the crossbar.
Arsenal had switched to a back four and the home side almost capitalised on the extra space when Tadic played in Ryan Bertrand, but the left-back's shot across goal just missed the far post.
However, after Alexis Sanchez had tested Forster with a 25-yard free kick, the Chilean quickly turned provider to set up Arsenal's leveller, with his cross finding Giroud who sent a glancing header into the far corner.
The goal was harsh on Southampton but, not for the first time this season, Pellegrino's side were made to pay for failing to take their chances.
As for Arsenal, they have now won just two of their eight away matches in the league this season but one consolation for Wenger was Liverpool being held by Everton in the Merseyside derby, a result which keeps the Gunners within touching distance of fourth place.
SOUTHAMPTON (4-4-1-1): Forster; Stephens, Van Dijk, Yoshida, Bertrand; Ward-Prowse, Hojbjerg, Romeu, Redmond (Boufal 74'); Tadic (Davis 88'); Austin (Gabbiadini 86')
ARSENAL (3-4-3) Cech; Koscielny, Mertesacker (Welbeck 64'), Monreal; Bellerin, Xhaka (Wilshere 69'), Ramsey, Kolasinac; Ozil, Sanchez; Lacazette (Giroud 72')