Chelsea required an 85th-minute winner from Ashley Cole to overcome Stoke City, Rickie Lambert was on target twice as Southampton claimed their first victory, and Hugo Rodallega haunted his old club.
New signings Shinji Kagawa and Robin van Persie were both on the scoresheet as Manchester United recovered from a goal behind to overcome Fulham 3-2 at Old Trafford.
Fulham winger Damien Duff has retired from international duty with the Republic of Ireland.
Swansea City and Fulham both recorded 5-0 victories over Norwich City and Queens Park Rangers respectively, while West Bromwich Ablion beat Liverpool and Newcastle saw off Tottenham Hotspur on day one of the 2012/13 Premier League.
Stand-in Republic of Ireland captain John O'Shea was positive following Republic of Ireland's 0-0 draw with Serbia, but felt they are still not performing to their full potential.
Damien Duff will mark his 100th cap for Republic of Ireland by leading them out in their UEFA EURO 2012 match with Italy tomorrow as they hope to get a win before exiting the tournament.