Everton looked set to settle for a point at Selhurst Park as they struggled to break down a stern Crystal Palace but Seamus Coleman provided the all important finish in the 87th minute.
The Toffees had the better chances throughout the game, several through Ross Barkley but Wayne Hennessey was equal to each effort.
The Welshman kept Everton out on a number of occasions, another notable one from Kevin Mirallas who took a shot on the volley from six yards out but it was too close to the keeper.
It took until the 87th minute, with Tom Davies playing through Irishman Coleman who shot over Hennessey to give Everton a massive three points.
Following Manchester United’s draw with Stoke City, Everton are now just five points behind 6th place in what looked like an impossible task only a few weeks ago.
The Toffees face Stoke, Bournemouth, Boro and Sunderland in their next four games as they look to crash the top six party.
