Giroud has largely been limited to cameo appearances since his winter move to Chelsea from Arsenal, and again on Saturday, manager Antonio Conte threw the France global on with less than half an hour to go.
"They must have great respect for the fans".
The France striker, who joined from Arsenal in January, then completed the sensational comeback 12 minutes from time, finding the bottom-right corner from 14 yards to secure all three points, and he acknowledged he has been itching to get off the mark.
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.
Dusan Tadic and debutant Jan Bednarek put the hosts in command, but Giroud struck either side of Eden Hazard's equaliser to cut the gap on Liverpool and Tottenham in the fight for a top-four finish and Champions League football next season to seven points.
Chelsea midfielder Danny Drinkwater recently suggested he will seek a move at the end of the season after starting just five Premier League games since his reported £35million move from Leicester City in August.
"Our first half was very negative". I don't understand why after 1-0 we always drop and let the opponent get more ball possession'.
Antonio Conte's men dominated the opening exchanges of the first half, although they struggled to carve out clear-cut chances. "If you don't have something in you're heart, it's hard to come back and win this game".
Southampton looked to be cruising towards a win that would have lifted them up to 17th and out of the relegation places, at least temporarily.
Those players are goal-scorer Eden Hazard, Willian, who provided two assists, and of course Olivier Giroud, whose introduction changed the game and ultimately won it for us. "I didn't say we were going to score, both me and him, but I thought if we score it might put them in a bad position". I think between the referee, linesman or fourth official that one of them should have seen it. Speaking about Chelsea's current status, Antonio Conte said in pre-match press conference that his side must do everything in their power to finish the season in the best possible way.