Arsenal showed the resilience that could underpin a Premier League title challenge when they scored twice in the closing minutes to draw 2-2 at Everton after the home side largely dominated the match on Saturday.
Aaron Ramsey tapped in after 83 minutes and substitute Olivier Giroud planted home a header in the 90th to cancel out the lead Everton held after a first-half header from Seamus Coleman and Steven Naismith's second on the stroke of halftime.
Chelsea, who beat Leicester City 2-0 at Stamford Bridge with goals from home debutant Diego Costa and Eden Hazard, and Swansea City, who sank Burnley 1-0 at the Liberty Stadium, head the early season standings with six points.
Arsenal stayed third 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.
In Saturday's other matches, West Ham United won 3-1 at managerless Crystal Palace, while the games between Aston Villa and Newcastle United and Southampton and West Bromwich Albion ended goalless.
Tottenham Hotspur, who host Queens Park Rangers, and Hull City, who welcome Stoke City, both on Sunday, can also move on to six points after winning their opening games as can champions Manchester City and runners-up Liverpool, who meet on Monday.
Arsenal's late Goodison Park rally was the second time this season they had scored late after Ramsey's 90th minute strike gave them a 2-1 win over visiting Crystal Palace last week.
It was also the second successive week Everton had conceded a late goal which denied them victory after allowing hosts Leicester City to equalise and force a 2-2 draw in their opener.
Arsenal manager Arsene Wenger told Sky Sports: "It is a strong point because we were 2-0 down but a deserved one."
He said the turning point was the introduction of Giroud for their new £35 million ($57.99 million) striker Alexis Sanchez at halftime.
"I thought we would dominate the game through the middle much more and Olivier had a very good second half," said Wenger who revealed Giroud had injured an ankle in the dying seconds and was a doubt for the Champions League playoff second leg against Besiktas on Wednesday.
Everton manager Roberto Martinez was naturally disappointed after conceding two late goals but said he was otherwise pleased with the way Everton performed.
"Certain individuals ran out of legs at the end and Arsenal, as you would expect, threw everything forward and the third goal was going to be vital.
"Obviously it's a disappointment but overall I am very pleased with the way we played."
Chelsea secured a second straight victory over a promoted team when they beat last season's Championship (second division) winners Leicester City 2-0 at Stamford Bridge thanks to second-half goals from Diego Costa and Eden Hazard.
Jose Mourinho's side started the season with a convincing 3-1 win at Championship runners-up Burnley on Monday but Saturday's triumph only came after a much improved second-half performance against resilient Leicester.
Mourinho was pleased with the way they improved after halftime, with Costa scoring his second in two games after 63 minutes from eight metres and Hazard adding a second 13 minutes from time with a low shot after cutting in from the right.
"We didn't play good in the first half," Mourinho told Sky Sports. "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.
"The second half was complete control. 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."
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.
The welsh side played well and secured the victory when Nathan Dyer scored after 23 minutes.