Christian Eriksen's goal shortly before halftime offered fourth-placed Tottenham a route back into the game but Sterling lashed home from close range in the 72nd minute.
Dusan Tadic capitalised on a limp first-half display from Chelsea to give Southampton the lead at St Mary's and when Jan Bednarek doubled their advantage on the hour mark, Conte's men appeared to be heading for their 10th Premier League defeat of the season.
Giroud and Pedro came on right after Chelsea went 2-0 down which was the start of Chelsea's comeback.
The Saints entered the match in 18th position in the table, and having not won a league game on home soil in 2018. He had spoken many times about how much he wanted to score his first league goal for his new club, even after he put in good, if goal-less (outside of the FA Cup) performances. I don't understand why after 1-0 we always drop and let the opponent get more ball possession.
"I was very angry from our first half", Conte said.
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And their frustration overspilled as tempers flared when Marcos Alonso was lucky to escape unpunished for raking his studs down Shane Long's calf. "The important thing is to play with a great intensity and fight from the beginning until the end". He said he is the first person to take responsibility for that as the coach. If you don't have something in your heart, it's very hard to come back and win.
"I'm the first to take the fault for the first half, but I repeat the second half my players deserve great credit".
Conte swiftly responded by hauling off the disappointing Alvaro Morata and Davide Zappacosta for Pedro Rodriguez and Giroud.
If you don't have something in your heart, it's very hard to win the game, but today I'm very happy with the second half, and very disappointed with the first.
Gary Cahill and Andreas Christensen were picked at the heart of Conte's defence and there was no room for former Roma player Antonio Rudiger due to comments that he made in the media.