Arsenal can leapfrog their local rivals to top spot later on Saturday as the Gunners aim to keep their 100 percent record going away to Bournemouth.
- Fofana left out for Leicester -
At the other end of the table, Manchester United remain bottom ahead of their huge clash against Liverpool on Monday. But Leicester are only one point better off after Che Adams came off the bench to score twice and further darken the mood around the King Power. Wesley Fofana was left out of Brendan Rodgers' squad as the Frenchman seeks to force through a move to Chelsea.
Leicester are the only Premier League club yet to spend any money in the transfer window, but may have to in the final 10 days of the window to ward off a difficult season. James Maddison's free-kick had put the Foxes in front, but Adams twice pounced on poor defending in the absence of Fofana to give Southampton their first win of the season.
The pressure is also back on Aston Villa manager Steven Gerrard after his side threw away a perfect start to lose 3-1 at Crystal Palace. Ollie Watkins opened the scoring for the visitors at Selhurst Park after five minutes, but Wilfried Zaha quickly levelled.
Zaha then put Palace in front at the second attempt after his penalty was saved by Emiliano Martinez. Jean-Philippe Mateta made the points safe 19 minutes from time.
Fulham remain unbeaten on their return to the top flight as Aleksandar Mitrovic's powerful header won a thrilling west London derby against Brentford 3-2. The home side stormed into a two-goal lead thanks to Bobby Decordova-Reid and Joao Palhinha, but for the second time this season Brentford fought back from 2-0 down through Christian Norgaard and Ivan Toney.
Mitrovic had the final say, though, when he rose highest to meet Kevin Mbabu's cross to send Marco Silva's men into fourth. Everton secured their first point of the season thanks to Demarai Gray's late equaliser to cancel out Brennan Johnson's goal for free-spending Nottingham Forest in a 1-1 draw at Goodison Park.