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Manchester United fanned the embers of their top-four hopes with a 2-0 win against visiting Everton.
Mikel Arteta's team are third with 61 points after 27 games, a point behind Manchester City.
Liverpool have 60 points with champions City on 59 and Arsenal on 58, all three teams having played 26 games.
Liverpool won 3-1 while Manchester City beat Everton 2-0 in an earlier match.
Second-placed Arsenal remain on 40 points, two behind Liverpool who beat Burnley 2-0 on Tuesday.
Manchester City slipped out of the top four as Tottenham Hotspur made up ground with a third consecutive victory, beating Everton 2-1 at home.
Sheffield are bottom of the table with just one win all season and have five points from 14 games.
Anthony Gordon scored the only goal in Newcastle's deserved 1-0 victory over Manchester United that propelled them up to fifth in the table on 26 points.
Trent Alexander-Arnold drilled in an 80th-minute equaliser with his right foot to deny City a 24th successive home win in all competitions.
Manchester United's campaign of woe continued with a 1-0 home loss to Crystal Palace but there were no such troubles for Arsenal who, along with Spurs, closed the gap to leaders City to one point with a rampant 4-0 win at Bournemouth.