Liverpool could only come away from Newcastle with a 1-1 draw despite Philippe Coutinho netting a superb opener at St James' Park.
Coutinho scored a spectacular effort on the half-hour mark when he picked up the ball on the edge of the area and curled a fine strike into the top corner.
But Liverpool's lead only lasted for six minutes with Joselu netting a fortunate equaliser for Newcastle after Joel Matip's tackle inadvertently sent the ball in off his leg.
The result leaves Liverpool seven points adrift of the top in seventh, with Newcastle two points back in ninth.
Arsenal made it four wins out of four at the Emirates Stadium in the Premier League this season with a 2-0 victory over Brighton.
Nacho Monreal and Alex Iwobi netted in each half to secure the win for Arsene Wenger's side, who move up to fifth in the table.
Arsenal could have opened the scoring after just a minute when Alexandre Lacazette rifled a strike from the edge of the box but broke through 15 minutes later, with Monreal firing a loose ball home.
Brighton's Solly March lashed a stinging strike from the edge of the area against the post but Arsenal gave themselves a two-goal cushion soon after the restart when the unmarked Iwobi producing a great finish after Alexis Sanchez had backheeled the ball into his path.
The pressure on Everton manager Ronald Koeman grew as Burnley condemned his misfiring side to a 1-0 defeat at Goodison Park.
Koeman dropped Wayne Rooney to the bench and started striker Oumar Niasse, one of five changes after the 2-2 midweek Europa League draw at home to Apollon Limassol.
But Everton again struggled to create chances and were behind with 22 minutes gone as Robbie Brady found Stephen Ward and he cut the ball back to Jeff Hendrick, who jinked away from Morgan Schneirderlin and fired a cool low finish beyond Jordan Pickford.
Everton huffed and puffed but were unable to find a way back into the match and were booed off the pitch by the frustrated Goodison Park faithful.