Patrick Kelechi, Lagos – Thomas Tuchel’s side are now five points behind leaders Arsenal having taken only seven points from their first five matches despite their evening on the south coast starting perfectly when Raheem Sterling netted his third goal of the season from close range.
But brave Southampton fought back through talented teenager Romeo Lavia, who blasted home from the edge of the area to lift a subdued St Mary’s.
Saints never looked back from there with Adam Armstrong firing home the winner in first-half added time to leave Ralph Hasenhuttl’s side above the Blues.
Southampton travel to Wolves as their fixtures become more favourable with Brentford, Aston Villa and Everton to follow.
Chelsea host West Ham in a Premier League London derby on Saturday at 3pm.