After their recent slip-ups against Tottenham and West Ham, many thought the Blues were down and out when Jan Bednarek added to Dusan Tadic's early opener at St Mary's to give the struggling hosts a comfortable lead at the hour mark.
With pressure building on coach Antonio Conte, the Blues looked set to see their hopes of a top-four finish in the Premier League disappear, but substitute Giroud emerged to pull one back in the 70th minute and keep them in the game.
2 - Chelsea have won a Premier League game from two goals down for the first time since August 2002 under Claudio Ranieri (3-2 v Charlton). Throwback. pic.twitter.com/k7HefQS0Fi— OptaJoe (@OptaJoe) April 14, 2018
Less than 10 minutes later, Conte's men were in the lead through a strike from Hazard and another from Giroud, earning a much-needed three points.
It is the first time the London side have come from two goals down to win a Premier League game since August 2002, when a team managed by Claudio Ranieri clawed their way back against Charlton.
They are chasing the Reds once again this term as well as Tottenham, but face a huge fight in achieving their target.
Chelsea are still seven points behind both Liverpool and Tottenham with just five games to go.