Giroud came on just after the hour mark and changed the entire course of the game by heading home from a Marcos Alonso cross.
Defeat is another body blow to the 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.
Giroud scored a perfectly placed header to half the deficit on the 70 minute mark. Ward-Prowse's deep free-kick was cleanly met by the full debutante Bednarek whose half-volley went past Courtois in goal for Chelsea.
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Southampton lie three points from safety and while Hughes appears to have made them more risky going forward - they had scored just 29 goals in 30 Premier League matches prior to his appointment - their defensive fragility, mental as much as physical, was exposed as soon as Giroud entered the fray. Southampton failed to clear their lines as the Blues delivered cross after cross. The French man finished low and hard into the corner from close range to get his double.
With a top four finish looking increasingly unlikely, Conte will be looking forward to seeing his team finish the season properly and look to get three points against a team fighting to survive in the Premier League.
Following the victory, the Blues move up to 60 points, just seven behind Liverpool and Tottenham who occupy the third and fourth positions respectively.
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