The day's action began at Goodison Park where relegation-threatened Everton defeated Champions League-chasing Manchester United by a goal to nil.
Anthony Gordon scored the only goal of the game in the first half to relieve some of the pressure on Frank Lampard.
Chelsea bounced back from two successive defeats in grand style, taking out their frustrations on Southampton at the Saint Mary's stadium with a six-goal romp.
In a ruthless first half, the Blues raced into a four-goal lead before the break thanks to Marcos Alonso, Mason Mount, Timo Werner and Kai Havertz. Mount and Werner added a goal each in the second half to complete the rout.
Thomas Tuchel's side will need such ruthlessness in front of goal if they are to overcome Real Madrid in the Champions League on Tuesday after losing their quarter final first leg 3-1 at home.
Arsenal's bid to secure Champions League football took a hit after losing 2-1 at home to Brighton and Hove Albion. Leandro Trossard and Enock Mwepu scored for the visitors while Martin Odegaard halved the deficit for the hosts. Arsenal remain in fifth place, level on points with fourth placed Tottenham Hotspurs.
Leeds United moved towards safety with a comfortable 3-0 win at fellow strugglers Watford. Raphinha, Rodrigo and Jack Harrison were all on target for Jesse Marsch's men, who are nine points clear of the relegation zone.
