Arsene Wenger's side looked set to suffer their sixth Premier League defeat of the campaign as the clock ticked down at St Mary's with them unable to muster a response to Charlie Austin's third-minute opener.
But Giroud, on for the luckless Alexandre Lacazette, expertly headed home Alexis Sanchez's left-wing cross two minutes from time.
It was the France international's 17th as a Premier League substitute – equalling former Manchester United favourite Ole Gunnar Solskjaer's record for the most scored at a single club, while only Jermain Defoe has more in the competition's history with 23.
"We are pleased with the point because it is always difficult to play here," Giroud told BT Sport, following his seventh goal in all competitions this term.
"I always try to bring something for the team. We were missing players in the box so I tried to bring it
"It was a good cross from Alexis. It's nice to come back because from the beginning of the second half we were pushing and pushing."
Arsenal could have suffered greater damage than Austin's smartly taken strike during a shambolic opening – not what Arsene Wenger had in mind after seeing Manchester United race into an early 2-0 lead at Emirates Stadium last weekend.
"The boss said we wanted to start strong but in the beginning of the game we have been caught behind our defence," Giroud observed.
"Charlie did well – he could have scored a brace but fortunately for us it was just 1-0."
Like Giroud, Austin has had to accept long spells on the bench this season, but now has five goals in three Premier League starts.
"We started really well, got the goal and should have got the second really," said the ex-Burnley man, speaking alongside Giroud.
"We can’t really play like we did in the second half. We camped in from minute one. There was good defensive play but if you give Arsenal one chance…
"If we get the second goal I think it's all over. One goal in the Premier League is not enough."