UPDATE 2-Soccer-Villa, Everton and Fulham hunt Europa places

* Villa and Everton share six goals

* Fulham come from behind to win at Manchester City

(Updates with details)

By Mike Collett

LONDON, April 12 (Reuters) - The race for Premier League places in next season's Europa League warmed up on Sunday when Aston Villa and Everton fought out a thrilling 3-3 draw and Fulham came from behind to win 3-1 at Manchester City.

With the top four places virtually guaranteed to be filled by England's Big Four of Manchester United, Liverpool, Chelsea and Arsenal, who all won on Saturday, Sunday's matches focused on the teams looking to qualify for places in UEFA's secondary competition.

Aston Villa's tilt at a place in the top four virtually ended with their failure to beat Everton, but they remain in the hunt for a Europa League spot along with Everton, West Ham United, Fulham, Tottenham Hotspur and Wigan Athletic.

Villa fought back twice from trailing by two goals at Villa Park to secure a point to stay fifth with 53 points, one clear of Everton who are sixth on 52.