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. Then comes West Ham (44), Fulham (43), Tottenham (41) and Wigan (41) followed by Manchester City (38). Despite ending a run of four successive league defeats, Villa have now gone 10 games in all competitions without a win. Everton raced into a 2-0 lead after 23 minutes with Marouane Fellaini side-footing a Leighton Baines cross home in the 19th and Tim Cahill heading the second four minutes later after his first header rebounded back off the bar. John Carew brought Villa back into it after 33 minutes when he scored from six metres, but Everton re-established their two-goal advantage with a stunning long-range shot from Steven Pienaar eight minutes into the second half. Everton had no time to take control, though, as Villa struck back two minutes later when James Milner crashed home a 30-metre freekick after Joleon Lescott fouled Carew. Lescott was punished again 12 minutes later when he kicked Stilian Petrov in the head attempting to clear the ball and Gareth Barry powered his penalty past Everton goalkeeper Tim Howard for the equaliser. CITY SLUMP Manchester City, who face elimination from this season's UEFA Cup after losing 3-1 to Hamburg SV in the first leg of their quarter-final on Thursday despite taking the lead through Stephen Ireland, did the same thing on Sunday. Ireland put City ahead with a well-struck goal after 28 minutes, but Fulham came back to win with two goals from Clint Dempsey after 50 and 83 minutes and one from former City player Dickson Etuhu, whose brother Kelvin was playing for City. "It was disappointing but there were reasons for it, we were missing a lot of players today," City manager Mark Hughes told Sky Sports News. Hughes kept Brazil striker Robinho, British soccer's most expensive signing, on the bench until the 64th minute, presumably to rest him before Hamburg visit Manchester City next Thursday.