The Blues failed to heed their opposition's early warnings when Ryan Bertrand broke forward on the left in the 21 minute.
But Giroud showed what he is capable of with a fearless 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. I think that was the first chance they have'.
Less positive news for Chelsea is the fact that Marcos Alonso could face a Football Association charge for a stamp on Shane Long that went unseen and unpunished by referee Mike Dean shortly before half-time.
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They are out of the playoffs for the fifth season in a row, and they own just one playoff series victory in the past 18 years. Apparently, the New York Rangers aren't the only tenant at Madison Square Garden without a head coach these days.
Chelsea looked destined to suffer a sixth defeat from nine league outings when Jan Bednarek put Saints 2-0 up after an hour, but Antonio Conte's decision to throw Giroud on from the bench proved a masterstroke.
The turnaround was complete with 12 minutes left when Giroud reacted quickest to loose ball to volley into the bottom corner.
The win narrows the gap between Chelsea and the top four to seven points, though that could be widened again should Liverpool and Tottenham win their respective matches on Saturday evening.
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His arrival from Arsenal in January was greeted with minimum fanfare, but Giroud didn't take long to win Chelsea supporters over with his work rate and selfless commitment to making his team and teammates better.
Chelsea have fought back from two-down to secure all three Premier League points.
Giroud scored a perfectly placed header to half the deficit on the 70 minute mark. Conte's "point of reference" played a key role in Hazard's equaliser before firing in the victor himself. 'But like the last few months we didn't and we concede.
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Saudi Arabia blames Iran for supplying projectiles for rebel missile attacks, a charge Teheran rejects. After examining the debris, the coalition said it determined it was a Houthi aircraft.
The abiding sense is of a club, once the envy of many in the Premier League, coming to the end of its cycle in the top flight.
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