Chelsea have maintained their 100 percent start to the new season.
Goals from Diego Costa and Eden Hazard saw them beat newly-promoted Leicester 2-0 at Stamford Bridge.
Swansea also made it two wins from two - Nathan Dyer got the only goal of the game as they beat Burnley at the Liberty.
Mauro Zarate got his first goal in a West Ham shirt as the Hammers came away from Crystal Palace with a 3-1 win.
Shane Long came close to opening his Southampton account but could do nothing to break the deadlock at St. Mary's where it finished Southampton 0 West Brom 0.
In the lunchtime kick-off Newcastle had defender Mike Williamson sent off late on in their scoreless draw at Aston Villa.
Everton currently head Arsenal by a goal to nil, with close to 40 minutes gone in the first half.
Results
- Southampton 0-0 West Brom
- Chelsea 2-0 Leicester
- West Ham 3-1 Crystal Palace
- Swansea 1-0 Burnley