Romelu Lukaku scored twice as Everton beat Leicester City 4-2 in an enthralling Premier League clash to keep their faint hopes of Champions League qualification alive.

An unbelievable first half started with Tom Davies netting after just 30 seconds, the joint-fastest Premier League goal this season.

But goals from Islam Slimani and Marc Albrighton ensured Leicester, who made five changes ahead of their huge Champions League quarter-final away to Atletico Madrid on Wednesday, were ahead by the time the match reached the 10-minute mark.

Everton fought back, though, Lukaku heading in midway through the half to score for a seventh consecutive home league game.

Another aerial effort, this time from Phil Jagielka, had Ronald Koeman's men in front at half time, before Lukaku's 23rd top-flight goal of the season sealed victory after the break.

Everton had only collected one point from crucial away matches with Liverpool and Manchester United coming into the game, but have now won seven home league fixtures in a row.

Koeman's men move level on points with sixth-placed Arsenal – who have played three games fewer – and seven behind Manchester City in fourth, while Leicester stay 11th after manager Craig Shakespeare's six-match winning streak since taking charge came to an end.

In a stunning start, Davies scored to celebrate signing a new contract with the club earlier this week.

Kevin Mirallas was the creator, surging past Daniel Amartey and Yohan Benalouane before being brought down on the edge of the area, with Davies making the most of the referee's advantage to take one touch and stab a left-footed finish inside Kasper Schmeichel's near post.

But Leicester were level in the fourth minute, Demarai Gray embarking on a magnificent run on the counter-attack from midway inside his own half and ultimately feeding Slimani to slot a cool finish through the legs of Joel Robles.

The visitors completed a remarkable turnaround inside 10 minutes after Jamie Vardy was fouled by Matthew Pennington, who started in place of suspended centre-back Ashley Williams. Joel and the home defence anticipated a cross and were caught out when Albrighton, who may not have meant it, whipped his free-kick into the top corner from an acute angle.

Joel got down to make a key save from Gray and an extraordinary game then took another twist when Ross Barkley's superb right-wing cross perfectly found Lukaku to guide in a header from six yards.

Mirallas and Robert Huth went head to head and earned bookings in a flashpoint caused by the Leicester defender's foul on the Belgium international, before Everton moved back in front in the 41st minute.

After Schmeichel raced out to deny Barkley one on one, defender Jagielka rose to head in the resulting corner - delivered by Mirallas - from close range.

Lukaku extended Everton's advantage 12 minutes into the second half. Barkley's corner deflected off Jagielka and Andy King, allowing the striker to fire home a right-footed finish at the far post and extend his lead over Harry Kane in the Golden Boot race to four.

Leicester introduced Riyad Mahrez, Ahmed Musa and Leonardo Ulloa from the bench but failed to test Joel in the second half until the keeper parried the Argentine's header in the closing minutes, with the Atletico match and the next chapter of the Foxes' remarkable story now awaiting them.