Eden Hazard levelled with an emphatic finish before Giroud - just eight minutes after his first - got a second to leave Saints deflated and defeated.
But Saints have struggled to hold on to leads this season and collapsed halfway through the second period, conceding three goals for the fourth successive league game.
SubstituteOlivier Giroud revealed that he urged Chelsea team-mate Eden Hazard not to give up against Southampton before the duo combined to complete a 3-2 comeback win at Southampton yesterday.
The Nigeria worldwide was thrown into the game in the 86th in place of Eden Hazard at a time when both teams were cautiously playing to see off regulation time.
I hope that the increasingly isolated Conte rests many first team players for the Thursday night trip to Burnley. Swansea couldn't make home advantage count against Everton, but also opened up a five-point lead on Southampton just above the relegation zone with a 1-1 draw.
However, Conte's opposite number Mark Hughes was unhappy that Alonso had escaped a red card and has called for the player to receive a retrospective ban ahead of next week's FA Cup semi-final between the two clubs. "When the momentum shifts against us we can't get a platform and wait until the momentum swings our way again".
It was a former Chelsea player who got Saints off to a ideal start as Ryan Bertrand burst past CesarAzpilicueta down Southampton's left before squaring for Tadic to apply a simple finish.
James Ward-Prowse nearly doubled Southampton's lead on 38 minutes following a well struck 28-yard strike which Thibaut Courtois parried away.
"Our first half was very negative", said Chelsea boss Antonio Conte.
"I really wanted the team to bounce back in the second half and obviously at the beginning it was not what we expected, but in football you always have the chance to step up and bounce back".
"But I saw a great reaction".
But we have had the right spirit to come back and win this game.
When Gary Cahill failed to cut out Ward-Prowse's whipped free-kick, league debutant Bednarek nipped in at the far post to slide home and double Saints' lead.
Conte swiftly responded by hauling off the disappointing Alvaro Morata and Davide Zappacosta for Pedro Rodriguez and Giroud.
That goal was quickly followed by the equaliser, with Willian's low cross from the left finding Hazard, who was able to take a touch before firing home from inside the area to spare his side's blushes.
Chelsea were not finished though, and scored their third three minutes later when Giroud stroked a loose ball into the bottom corner to break Southampton hearts.
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