James Ward-Prowse's rocket and a Lucas Digne own goal gave Southampton a precious three points against Everton at St Mary's.
Leicester City suffered a 2-1 loss at home to lowly Southampton, leaving Claude Puel to face questions over his future at the club.
Pierre-Emile Hojbjerg apologised for getting sent off against Manchester City, with his manager calling his actions "silly".
David Silva and Sergio Aguero helped to get Manchester City back on track as Pep Guardiola's defending champions beat Southampton 3-1.
Pep Guardiola has called on experienced campaigners as Vincent Kompany, Fernandinho and David Silva all return for Man City at Southampton.
Felipe Anderson scored two exceptional goals as West Ham came from behind to beat Southampton.
West Ham came from behind to beat Southampton thanks to Felipe Anderson's stunning double.
Southampton boss Ralph Hasenhuttl greeted the 3-1 win at troubled Huddersfield Town as "very important" to the club's fight for survival.
Huddersfield Town slumped to a fifth straight Premier League loss as Southampton proved too strong at John Smith's Stadium on Saturday.
Ralph Hasenhuttl admitted beating Arsenal for his first victory as Southampton manager was a moment to remember.