(CNN) -

We are only two games into a new English Premier League season, but with seven minutes to go in their match against Everton, some Arsenal fans may have been quietly writing off their team's title chances.

They also may well have pondered what had changed from last season.

In the corresponding fixture last April, Arsenal were thumped 3-0 by Roberto Martinez's side and as the clock ticked towards full time at Goodison Park on Saturday the same result looked on the cards.

After being harried and hurried by Everton, the Gunners found themselves two goals down and staring down the barrel before the game was turned on its head with late goals from Aaron Ramsey and Olivier Giroud.

Everton had assumed control of the match with two first-half goals. Gareth Barry's cross was headed in at the far post by Seamus Coleman in the 19th minute and on the stroke of halftime Steven Naismith doubled the lead as Everton caught the visitors on the counterattack.

Romelu Lukaku brushed off a challenge from Per Mertesacker to break down the right before laying on a pass for the advancing Naismith to slide home under goalkeeper Wojciech Szczesny.

Television replays showed that Naismith was marginally offside but while Arsene Wenger flapped his arms in protest the Goodison Park faithful celebrated.

Everton's industrious midfield continued to thwart Arsenal's advances in the second half before the Gunners fired their late salvo.

Ramsey toe-poked Santi Cazorla's low cross past Tim Howard in the 83rd minute to net his fourth goal in five matches before Olivier Giroud, who replaced new signing Alexis Sanchez at halftime, headed home to make it 2-2 in the final minute of normal time.

In the four added minutes, Arsenal looked as though they might snatch all three points but it ended honors even.

The draw maintains Arsenal's unbeaten start to the season and lifts them to third in the table with four points following a 2-1 win against Crystal Palace on the opening weekend of the season.

Everton have two points from two games and are 10th.

Earlier in the day, Chelsea maintained their 100% start to the season with a 2-0 win against Premier League new boys, Leicester City.

Second-half strikes from Diego Costa and Eden Hazard earned Jose Mourinho's side all three points to keep the West Londoners at the top of the table on goal difference.

Swansea City and West Ham United were also winners on Saturday.

After beating Loius van Gaal's Manchester United 2-1 at Old Trafford last weekend Garry Monk's side bagged another three points with a 1-0 win at home to Burnley.

West Ham opened their account with a 3-1 win at Crystal Palace after losing to Tottenham Hotspur on the opening day of the season.

The games between Aston Villa and Newcastle United and Southampton and West Bromwich Albion ended in goalless draws.