Arsenal were again undone at Stoke in the Premier League, with Mark Hughes' side winning 1-0 thanks to a debut goal from Jese Rodriguez.
Manchester United had no such trouble, thrashing Swansea 4-0 in south Wales.
Liverpool beat a stubborn Crystal Palace with the game's only goal.
Southampton needed an injury-time penalty to secure a 3-2 win over 10-man West Ham, who had come from 2-0 down.
Burnley were beaten 1-0 at home by West Brom, while Leicester won against Brighton and Watford beat Bournemouth - both games were 2-nil.