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.
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However, Everton's four point lead was restored when they beat Manchester United and Burnley lost at Norwich - a result that prompted the shock dismissal of Sean Dyche. For much of Sunday afternoon's match it appeared as though Burnley would gain an immediate bounce under caretaker boss Mike Jackson.
They had overcome the sight of key midfielder Ashley Westwood being stretchered off with what appeared to be a serious injury midway through the first half - an incident that left Nikola Vlasic, who Westwood had collided with, in tears. Yet Cornet's penalty miss prevented the visitors from doubling their lead just before the break. Soucek was then able to level after 74 minutes.
The 1-1 draw means Everton are now three points clear of Burnley with a game in hand. The Blues host Leicester City on Wednesday before Burnley play Southampton at Turf Moor 24 hours later in the next instalment of the relegation battle.
