Defeat is another body blow to Saints’ chances of avoiding relegation as they remain rooted in the bottom three when for so long they seemed set for a first home win in the Premier League since November.
Dusan Tadic and debutant Jan Bednarek put the hosts in command, but Giroud’s first league goals for Chelsea either side of Eden Hazard’s equaliser cut the gap on Liverpool and Tottenham in the fight for a top-four finish to seven points.
The two sides will meet again in the FA Cup semi-finals next weekend, and Southampton will do well to raise themselves for cup glory with their place in the Premier League next season looking ever more precarious.
It was a former Chelsea player who got Saints off to a perfect start as Ryan Bertrand burst past Cesar Azpilicueta down Southampton’s left before squaring for Tadic to apply a simple finish.
Only a fine save low to his right from Thibaut Courtois denied Saints a second through James Ward-Prowse as Chelsea struggled to create anything of note before the break.
And their frustration overspilled as tempers flared when Marcos Alonso was lucky to escape unpunished for raking his studs down Shane Long’s calf.
Long nearly doubled Southampton’s lead early in the second period when he turned Andres Christensen and Gary Cahill before his mishit effort almost looped over Courtois, who scrambled to turn the ball behind.
Courtois was left exposed by his defence moments later when Ward-Prowse’s free-kick found Bednarek completely unmarked at the back post to half-volley expertly across the goal and into the far corner.
Conte swiftly responded by hauling off the disappointing Alvaro Morata and Davide Zappacosta for Pedro Rodriguez and Giroud.
The French international striker has largely struggled to make an impact since his deadline day move from Arsenal in January.
But Giroud showed what he is capable of with a brave near post header from Alonso’s pinpoint cross to get Chelsea back in the game with his first league goal for the club and spark an incredible fightback 20 minutes from time.
Five minutes later Hazard levelled by smashing home Willian’s cross from close range.
And with Southampton reeling, Giroud completed Chelsea’s comeback when he pounced on a loose ball inside the area to drive into the bottom corner.
Chelsea still needed Courtois to secure just a fourth league win in 12 games in 2018 as the ‘keeper got down well to deny Josh Sims as the game entered stoppage time.