Arsenal scored twice in the last seven minutes to escape with a 2-2 draw at Everton on Saturday after the home side had largely dominated the Premier League encounter at Goodison Park.
Aaron Ramsey scored after 83 minutes and substitute Olivier Giroud planted home a header in the 90th to cancel out the lead Everton held after first-half goals from Seamus Coleman and Steven Naismith.
The result meant Arsenal stayed third in the early-season table with four points from two games although their run of six successive league victories, which started after they lost 3-0 at Everton in April, came to an end.
Chelsea, who beat Leicester City 2-0 at Stamford Bridge, and Swansea City, who sank Burnley 1-0 at the Liberty Stadium, head the standings with six points.
In the day's other matches West Ham United won 3-1 at Crystal Palace while the games between Aston Villa and Newcastle United and Southampton and West Bromwich Albion both ended goalless.
Chelsea secured a second successive win over a newly-promoted side, thanks to second-half goals from Diego Costa and Eden Hazard.
West Ham United picked up their first points 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.
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."
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