Everton's main relegation rivals threw away a golden opportunity to move to within one point of the Blues.
Burnley's Maxwel Cornet missed a penalty with the Clarets already leading by a goal at West Ham. But he dragged the effort wide and the home side fought back to level through Tomas Soucek.
The miss could prove pivotal in a relegation battle during which momentum has swung between Everton and Burnley over weeks of drama. Cornet had scored the late winner that dragged Burnley within touching distance of Everton when they beat the Blues 3-2 at Turf Moor earlier this month.
