Conte managed to change Chelsea's fortunes by bringing on Olivier Giroud who scored two goals, either side Eden Hazard's strike, as Chelsea ran out 3-2 winners. They sit three points away from the safety of the 17th slot, which is now held by Crystal Palace.
Chelsea's French attacker Olivier Giroud (R) celebrates scoring their third goal with team-mates Chelsea's Brazilian midfielder Willian (L) and Chelsea's English defender Gary Cahill (C) during the English Premier League football match between Southampton and Chelsea at St Mary's Stadium in Southampton, southern England on April 14, 2018.
Chelsea are now 10 points shy of London rivals Tottenham, who occupy the final Champions League qualification place, but Hazard is not ready to give up the chase yet.
Jan Bednarek, making his first start for Saints, then doubled the hosts' lead in the 60th minute, leaving Chelsea facing the prospect of a sixth league defeat in nine matches.
"We got ourselves into a great position".
It was no surprise that they drew first blood with their first attempt at goal when Dusan Tadic made a late entry to the box to tap home Ryan Bertrand's cross on 21 minutes.
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In fact, no team has won back-toback Premier Leagues since Man United in 2008 and "09, highlighting its difficulty". Perhaps the only major negative of City's season was our defeat to Liverpool in the Champions League quarter-final.
Southampton will hope to keep their survival hopes alive this weekend but it'll be easier said than done as they'll take on a Chelsea side who are still in with a shout of making it into the top four.
Hazard began to inject some life into Chelsea's play, causing several problems in and around the area without troubling the goal itself.
"Southampton played a good game and took a lot of confidence after their first goal because they were nervous at the start". We went 2-0 down but had the right spirit to come back and win. I said in the second half that we must be pleased because I saw the right fire and desire in my players.
Amid that backdrop, Conte has told his players they must play for the club, rather than for him, over the next few weeks.
Conte added, "I was a player, and the players must play every game, and not for me, but for the club, and for the fans". - The Blues have won five in a row against Saints in the league for the first time ever.
"If we defend like we did today from set pieces then we could find ourselves two or three down and we're not going to get back in the game".