The win kept Chelsea in fifth on 60 points, seven points adrift of fourth-placed Tottenham who will face Manchester City later on Saturday.
Goals from Dusan Tadic and debutant Jan Bednarek had put Saints on the way to a crucial three points but Giroud headed a previously listless Chelsea back into a game that had appeared nearly out of reach, Eden Hazard levelled shortly afterwards and then the France hitman struck again - all inside an eight-minute spell.
"The first half wasn't good, not only from tactical aspect", the Italian told Sky Sports. I have been through difficulties in my career, other times I tried to come back stronger.
Southampton stayed in the relegation zone with five games left, and manager Mark Hughes was aggrieved that Alonso avoided punishment for a studs-up challenge on Shane Long in the first half. It doesn't matter that we won the game 3-2, it was important to see the right reaction and fight in the eyes of my players. They played so well for the first 69 minutes and deserved to lead 2-0, but the substitute Olivier Giroud inspired another insane comeback in this memorable week of football. We need to finish this season in the best possible way. "He says he was 'very angry" with our first-half performance, ' believing they lacked desire and will to fight.
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The home side had already raced to a two-goal lead before Antonio Conte moved to take out Alvaro Morata for Giroud.
"I must be honest, I didn't see this", Conte said.
And although Conte was impressed with the comeback - the first time Chelsea had come from two goals down to win a league game since 2002 - he was keen to ensure people knew his opinion of their first-half display.
Given the earlier scoreline, it really should have been game over, given that the Blues hadn't come back to win from 2-0 down in a Premier League game in 16 years. "He has specific characteristics, he played well and I am happy for him".