Chelsea 2 - 0 Leicester
A Villa 0 - 0 Newcastle
C Palace 1 - 3 West Ham
Southampton 0 - 0 West Brom
Everton 2 - 2 Arsenal
Swansea 1 - 0 Burnley
Ten-man Newcastle registered their first point of the new season after fighting out a 0-0 draw with Aston Villa in the lunchtime kick-off.
The game at Villa Park was one of few real chances, particularly in the first half, with Magpies midfielder Remy Cabella sending one wide when he might have done better.
The visitors had further opportunities just after the break, with Daryl Janmaat having a header pushed over by Villa goalkeeper Brad Guzan and firing a shot just off-target.
Magpies substitute and debutant Siem de Jong was then denied by a decent Guzan save towards the end, before Mike Williamson was sent off in the final seconds having collected two yellow cards in quick succession.
Everton threw away two valuable points at Goodison Park as Arsenal striker Olivier Giroud scored a last-minute header to secure a dramatic 2-2 draw.
Roberto Martinez's side looked to be coasting to an easy 2-0 win thanks to goals from Seamus Coleman and Steven Naismith, but their defence crumbled in the final minutes to gift the Gunners a point.
First, Aaron Ramsey bundled home a Santi Cazorla cross and then, with 30 seconds to go, Giroud headed past Tim Howard thanks to some sloppy marking from Sylvain Distin.
It was a cruel blow to Everton, who really should have secured an early blow over their rivals in the hunt for Champions League qualification.
Diego Costa opened the scoring as Chelsea made it two wins in a row to open theirPremier League campaign with a 2-0 triumph over Leicester at Stamford Bridge.
The Spain striker, who opened his account with a goal on debut in the Blues' 3-1 opening victory at Burnley on Monday night, pounced again from inside the penalty box to put Jose Mourinho's side ahead against the promoted visitors just after the hour.
Eden Hazard added a second goal with an effort 13 minutes from time to put the result beyond doubt, with the biggest cheer of the day reserved for the late introduction of Didier Drogba in place of Costa.
Nathan Dyer's goal earned Swansea a 1-0 victory against Burnley at the Liberty Stadium.
The winger latched on to a superb through-ball from Gylfi Sigurdsson and coolly slotted home midway through the first half to continue the Swans' 100 per cent start following last weekend's success at Manchester United.
Managerless Crystal Palace went down 3-1 at home to West Ham.
Mauro Zarate, Stewart Downing and Carlton Cole were the men on target for Sam Allardyce's side, who notched their first victory of the season following their last-gasp home defeat to Tottenham.
Marouane Chamakh had halved the deficit for the Eagles just after the break, but it proved to be in vain.
Southampton and West Brom remain in search of their first wins after battling out a goalless draw at St Mary's.
This was the first top-flight home game in charge for new Saints boss Ronald Koeman and he left with a point.