(Adds later games)
Manchester City opened up an 11-point gap over champions Chelsea when they beat Crystal Palace 1-0 with a stoppage-time goal at Selhurst Park after Chelsea crashed to a 3-1 defeat at Everton.
City looked set to drop their first points of the season until teenage substitute Kelechi Iheanacho struck late at Selhurst Park.
Manuel Pellegrini's team moved to 15 points from five matches and they top the table from Arsenal, who grabbed their first home win and goals of the season with a 2-0 victory over Stoke City to move up to 10 points. Theo Walcott and Olivier Giroud were on target.
Palace are third with nine points, one ahead of Everton, at least until Manchester United and Liverpool meet in the late match at Old Trafford.
Everton's Scotland striker Steven Naismith bagged a hat-trick after coming off the bench in the ninth minute against the floundering Chelsea who are 16th in the table with four points.