Manchester United and West Ham also won their games to put pressure on Arsenal
Roberto Martinez's Everton future has been plunged into further doubt as Liverpool thrashed his side in the Merseyside derby.
Jurgen Klopp's team ran out 4-0 winners at Anfield against Everton's 10-men to move up to 7th in the Premier League table.
Divock Origi headed in Liverpool's opener two minutes before half-time as he met James Milner's in-swinging cross.
Mamadou Sakho doubled that lead when he turned his free header in first half stoppage time.
Five minutes after the break, it went from bad to worse for Everton after defender Ramiro Funes Mori's nasty challenge caught Origi on the ankle, earning himself a red card and forcing the Belgian striker to be stretchered off.
With the man advantage, Daniel Sturridge added a third, before the icing on the cake from Philippe Coutinho who curled in from the edge of the box.
Manchester United's Wayne Rooney with Crystal Palace's Emmanuel Adebayor after the final whistle during the Barclays Premier League match at Old Trafford, Manchester. Picture by: Martin Rickett / PA Wire/Press Association Images
For Everton, they are now without a Premier League win since March 1st as the pressure piles on Martinez.
Meanwhile, West Ham were 3-1 winners over 10-man Watford at Upton Park.
Andy Carroll got the opener for the home side before Mark Noble scored twice from the penalty spot.
And Manchester United prepared for their FA Cup semi-final against Everton with a 2-0 win over Crystal Palace at Old Trafford.
An own-goal from former Irish international Damien Delaney gave United the lead before Italian defender Matteo Darmian made sure of the points in the 55th minute.