Chelsea secured a second successive win over a newly-promoted side when they beat Leicester City 2-0 at Stamford Bridge on Saturday thanks to second-half goals from Diego Costa and Eden Hazard.
Jose Mourinho's side started the season with a 3-1 win at last season's Championship (second division) runners-up Burnley on Monday and Saturday's win over winners Leicester gave them six points after a much improved second-half performance against the resilient visitors.
Swansea City also have six points from their opening two games and are second behind Chelsea in the early-season table after beating Burnley 1-0 at the Liberty Stadium.
West Ham United picked up their first points with a 3-1 win at managerless Crystal Palace thanks to two first half goals in three minutes from Argentine debutant Mauro Zarate and Stewart Downing, and a second half volley from Carlton Cole.
Marouane Chamakh scored for Palace before Cole's third for the Hammers but the Eagles have now lost both their opening games following their 2-1 loss at Arsenal last week.
In the other games Aston Villa drew 0-0 with Newcastle United in a dour match and Southampton were held to a 0-0 draw at home by West Bromwich Albion.
Chelsea manager Mourinho was pleased with the way his team improved after half-time with Costa scoring his second goal in two games after 63 minutes with an eight-metre shot and Hazard adding the second 13 minutes from time with a low shot after cutting in from the right.
"We didn't play good in the first half. Leicester came with great defensive intensity, trying to scare us on the counter-attack and we were a bit slow – slow in moving the ball and slow thinking and we needed to change and we did that," Mourinho told Sky Sports afterwards. "The second half was compete control. I don't forget they had a good chance with the result 0-0 but we had so many chances, so many opportunities to score obviously we deserved the victory."
Leicester boss Nigel Pearson said he was disappointed, explaining: "Key moments didn't quite go our way today. I thought we played exceptionally well in the first half but it's about taking your chances when you get them.
"There are more positives today than there are negatives. We're not talking about us coming to places like this and being happy to lose the game, but I think the players showed what they're capable of. What we need to do is sustain it for the entirety of the game."
Swansea, who opened their campaign with a first ever league win at Manchester United last week, picked up another three points against a battling Burnley side.
"I knew it would be a tough game. In the first half we controlled it, but in the second we expected them to throw everything at us and they did,” Swansea manager Gary Monk told Sky Sports.
