The fight for fifth place in the Premier League and the last remaining Uefa Cup spot is set to go to the final day of the season after a dramatic and pulsating showdown at Goodison Park between the sides fifth and sixth in the table.

Everton led twice, through Phil Neville’s deflected effort and Joseph Yobo’s crisp close-range finish, but Villa just refused to give up the chase, and Gabriel Agbonlahor and John Carew grabbed vital equalisers in a remarkable late spell of three goals in six minutes.

The Merseysiders still hold a three-point lead, though Villa have a better goal difference and a slightly easier-looking run-in, with Wigan Athletic at home and West Ham United away, on the last day. Everton must still face Arsenal at the Emirates with Newcastle United visiting Goodison in their final match.

Aston Villa, with 15 goals in their last three matches, were unstandably brimming with confidence, and Gareth Barry, occupying a floating role on the left, and Carew saw efforts go wide, Villa having the better of much of the first period midfield exchanges.

Everton’s best effort in the early stages came when Ayegbeni Yakubu surged down the left, holding off and then bustling past Nigel Reo-Coker before firing in a shot that Scott Carson could only palm out, with Manuel Fernandes mis-hitting his effort badly wide as he tried to fire home the rebound, a rare clear opening at that stage against Villa’s solid back-line.

Carew’s clever chip almost put Ashley Young clear in the box, before the former Watford player crashed a free-kick against the crossbar after Phil Jagielka’s rash challenge on Agbonlahor.

For Everton, Andrew Johnson’s right-sided run created yards of space, but his low cross was behind both Steven Pienaar and Yakubu as they raced into the box.

With the tackles still flying in, referee Phil Dowd was inevitably soon involved. Stiliyan Petrov was booked for a late challenge on Osman before Yakubu was cautioned for dissent and Lee Carsley saw yellow for a lunge at Petrov.

Everton emerged after the break with genuine purpose, looking for width and pace to unsettle Villa’s defence. Olof Mellberg, Martin Laursen and Zat Knight had given very little away, but after 56 minutes they were undone by Yakubu’s strength.

The Nigerian’s first touch sent him powering away from Knight on the left, and although his cross was wayward the ball fell into Neville’s path 25 yards out on the opposite flank.

It would have been easy to lash the effort over the bar, but Neville coolly converted for his second goal of the season, his shot flicking off Laursen’s chest and wrong-footing Carson.

After 65 minutes, David Moyes, the Everton manager, took off Fernandes and brought on Mikel Arteta, who had not trained for a fortnight after injury and only arrived back from Spain on Saturday.

Villa sent on attacking players Patrik Berger and Marlon Harewood for defenders Knight and Wilfred Bouma, the need for goals now critical for Villa’s European dreams. And after 80 minutes they succeeded. Barry’s corner swirled into the box and Agbonlahor was free eight yards out to side-foot the equaliser past Tim Howard.

Everton’s response was to inject the extra strength and height of Victor Anichebe for Johnson after 82 minutes. It came two minutes later when Carsley’s clipped cross to the far post was met by Yobo, who slammed the ball into the roof of the net.

Everton thought they were home and dry, but two minutes later Villa were level again, Barry’s cross being headed in by Carew, who outmuscled Joleon Lescott to get to the ball first.

Harewood and Anichebe were booked after a flare-up on the touchline in a pulsating finale.