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Roberto Firmino scored a late equaliser in his last home game for Liverpool to salvage a 1-1 draw for his side against Aston Villa that just about kept their hopes of a Premier League top-four finish alive on Saturday.
Liverpool had won seven games in succession to make a late run for Champions League qualification but defeat by Villa would have guaranteed that Newcastle United and Manchester United finish in the top four.
While Liverpool's hopes of qualifying for the Champions League look slender, Merseyside neighbours Everton are fighting for their top-flight lives after a 69-year stay as Yerry Mina secured them a point at Wolverhampton Wanderers with an equaliser in the ninth minute of stoppage time.
Everton were headed for damaging defeat as they trailed to a Hwang Hee-chan goal at Molineux but Mina's goal lifted them two points clear of the relegation zone with one game left.
The two sides immediately below them -- Leeds United and Leicester City -- would both move above Everton if they win their next games, but whatever happens the relegation battle will go down to next Sunday's season finale.
In the day's final fixture Arsenal must avoid defeat at Nottingham Forest to stop Manchester City being crowned champions ahead of their home game against Chelsea on Sunday.
Forest would secure safety with a win.
Villa led at Anfield thanks to Jacob Ramsey's headed goal in the 27th minute, five minutes after they had squandered the chance to open the scoring when Ollie Watkins missed a penalty.
Liverpool's top-four hopes looked over with Manchester United winning at Bournemouth, but Brazilian Firmino, making his Anfield farewell after eight glorious seasons, struck an equaliser in the 89th minute after coming off the bench.
Even the point leaves their chances wafer thin, though, as fourth-placed Manchester United and third-placed Newcastle United have 69 points with two games left while Liverpool have 66 with only one game remaining.
Casemiro's superb acrobatic volley was enough for Manchester United to win 1-0 on the south coast and one more point from their last two games will guarantee them Champions League football.
Newcastle can seal their return to Europe's elite competition after a two-decade absence if they take a point against relegation-threatened Leicester on Monday.
Firmino's late goal left Villa in seventh place with 58 points, below Brighton & Hove Albion on goal difference although Brighton are in pole position to claim a Europa League place as they have three games still to play.
Tottenham Hotspur slipped down to eighth with 57 points as they surrendered an early lead given to them by Harry Kane's superb free kick to lose 3-1 at home to ninth-placed Brentford for whom Bryan Mbeumo scored twice in the second half.
Fulham drew 2-2 at home to Crystal Palace.
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