Manchester United and Newcastle will have to wait to secure a place in the Champions League for next season after Roberto Firmino kept Liverpool in the race with a late equaliser against Aston Villa.
Liverpool had put pressure on United and Newcastle by putting together a run of seven straight wins, but looked to be faltering against Aston Villa. United beat Bournemouth 1-0 in their 3pm kick-off on Saturday and appeared to be heading four points clear of Liverpool ahead of the Reds' final game of the season last weekend.
Jacob Ramsey's first-half goal, and Cody Gakpo's ruled-out equaliser, had Villa heading for a 1-0 win. But Firmino came off the bench to score from Mohamed Salah's cross in the 90th minute to ensure Liverpool still have an outside chance of finishing in the top four.
United and Newcastle remain three points ahead of Liverpool with two games left to play, meaning both clubs need just one more point to see off their challenge.
After Ollie Watkins sent a penalty wide, Villa took the lead through Ramsey midway through the first half. Jurgen Klopp's side thought they had equalised through Gakpo, only for VAR to rule it out for offside against Virgil van Dijk in the build-up.
Klopp was absent from the sidelines, due to a two-match ban, but his coaching staff were furious with the decision, that came after referee John Brooks watched replays on the pitchside monitor.
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After a miserable first half of the season, Liverpool did well to fight back and push United and Newcastle, but their dream of returning to the Champions League is now hanging by a thread. They are still likely to play in the Europa League next season, with fifth place secure thanks to a five-point gap to Villa.
Casemiro scored the game's only goal at the Vitality Stadium, with David de Gea producing some excellent saves in the second half to secure the points. By contrast, things did not go to plan for Liverpool at Anfield.
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United and Newcastle are both on 69 points with two matches left to play and now can't be caught by Liverpool, who are on 66 points and face Southampton on the final day of the season next weekend.
Eddie Howe's side face Leicester at St James' Park on Monday before finishing their season away to Chelsea on Sunday. They are currently in third, ahead of United in fourth, thanks to a vastly superior goal difference.
United host Chelsea at Old Trafford on Thursday and play Fulham at home on the weekend before facing Manchester City in the FA Cup final on June 3.