The first opportunity fell Everton's way in the sixth minute when Seamus Coleman's through-ball made its way to Steven Pienaar. The South African just had Wojciech Szczesny to beat but lifted his shot high over the crossbar.
A scrappy quarter of an hour followed before Marouane Fellaini underhit a clearance straight to Santi Cazorla on the edge of the area. The Spaniard laid it on once more to Kieran Gibbs but the full-back's shot rose over.
It wasn't until the 39th minute when the first shot on target came. Ross Barkley's effort from outside the area was easily held by Szczesny.
Moments later the Toffees came closer when Barkley turned cleverly in the middle and fed Victor Anichebe. The striker was challenged upon shooting but the ricochet almost squeezed under the dive of Szczesny.
Victory for Everton this evening could see them rise into the European places.