Diego Costa bookended an extraordinary end-to-end contest at Goodison Park with goals in the first and last minute to help Chelsea see off Everton and claim a thrilling 6-3 victory and maintain their perfect start to the Premier League season.

In a match that will live long in the memory thanks to goals, officiating errors and physical confrontations aplenty, Everton three times reduced a two-goal deficit to one as they time and again threatened to make spectacular comebacks. But each time they did, Chelsea found another gear to extend their advantage once more.

Even after Ramires scored to make it 5-3 with 13 minutes remaining at the end of an extraordinary 10 minute spell that featured five goals, it took a spectacular save from Thibaut Courtois to turn a Kevin Mirallas shot onto the post and prevent even greater drama late on. Costa’s late goal added an emphatic sheen to the victory that was perhaps harsh on the hosts after such a spirited performance.

The breathless action had begun right from the off when Costa and then Branislav Ivanovic put Chelsea two goals to the good inside four minutes, although with the second owing much to a assistant referee's failure to raise his offside flag. Impressively Everton recovered their composure and Mirallas’s brilliant header right before half time ensured the second half would be no damp squib. Then came the ridiculous spell as first a Seamus Coleman own goal and then a fierce Nemanja Matic strike had given Chelsea breathing room, only to be pegged back immediately on each occasion, courtesy of strikes from Steven Naismith and on his debut, against his former club, Samuel Eto’o. But Ramires and then Costa finally ensured that the three points would be heading back to Stamford Bridge and Chelsea would be top of the table.

While the entertainment was nonstop for the neutrals, both managers will doubtless have stern words with their players for their inability to keep the ball out of their own net. Despite the win, Jose Mourinho -- a manager who relishes a clean sheet perhaps more than any other -- will be far from happy, while Roberto Martinez will be alarmed at the continuation of Everton’s defensive woes at the start of the season. Having given up leads to draw 2-2 against Leicester City and Arsenal, the problems at the back resurfaced right from the off.

There had been plenty of scare stories leading up to the match that Costa had suffered a potentially serious hamstring injury in training. It took just 34 seconds for him to put those doubts to bed. Chelsea’s big two summer signings gave a perfect demonstration of the more incisive threat they were recruited to provide. Playing in a more advanced role, Cesc Fabregas found a pocket of space and was allowed to look forward unhurried. Phil Jagielka committed a cardinal sin of attempting to push up without pressure on the ball, Costa’s run was timed perfectly in behind and he finished low through the legs of Tim Howard.  

Despite Everton’s appeals, the officials had been right to not raise a flag on that occasion. Not so just over two minutes later when a shell-shocked Everton fell two behind. Again Everton failed to close their opponents down, but this time they were harshly done by as Ramires’s pass found Ivanovic just marginally behind the last defender. Still, the right-back showed impressive poise in front of goal to shoot under Howard and get his second goal in the first three games of the season.

The testing 45 minutes for the official continued and they again failed to cover themselves in glory. As he raced out to try and prevent Eden Hazard getting onto a through ball, Howard clearly grabbed the ball outside his area, but, to his obvious relief, the American escaped sanction. At the other end, Romelu Lukaku, looking to show his former club what they were missing out on, crashed a header against the crossbar and Sylvain Distin was rightly called offside as he turned in the rebound.

But Everton were showing plenty of character to begin finding their passing rhythm after such a bitterly disappointing start. The only problem was trying to break through what, at that stage, was a resolute Chelsea defense. Then seconds before halftime they broke Mourinho’s men down. A fine move culminated with Coleman supplying an excellent cross and Mirallas meeting it with an even better header to direct the ball into the corner.

The goal set the stage for an incredible second half. After Lukaku wasted a chance to equalize, Costa forced Howard into a brilliant low save. By that point Costa was beginning to live up to the pantomime-villain status he had cultivated in La Liga in a running battle with Coleman. That feud spilled over when Coleman turned Hazard’s cross into his own net following a stunning burst of pace from the Belgian. Costa took the opportunity to taunt the Irish defender and Howard reacted furiously, earning a yellow card for his troubles.

The goal was just the start of a manic spell. With a wonderfully clever poked finish, the excellent Naismith brought Everton back to within a goal once more just two minutes later. Just five more minutes passed before Matic drove a left-footed effort past two defenders from the edge of the box, only to see Eto’o, having just come on for his first appearance for Everton after being released by Chelsea, direct a fine header into the corner.

Goodison Park was buzzing and imploring their team to fight for a point that would be welcomed much more favorably than those secured in their first two games of the season. But Everton just couldn’t keep the ball out at the other end. No sooner had they reduced their arrears, Everton were two behind once more when Ramires played an easy one-two with Matic and poked the ball past Howard. Had Mirallas’s instinctive volleyed flick not been somehow turned onto the post by Courtois then the comeback may have been on, but Costa ran through in the final minute to finally put the result beyond doubt.