Former Claret duo Dwight McNeil and James Tarkowski came back to haunt their old side when they combined for the opening goal before Amadou Onana and Ashley Young bagged after the interval - ensuring it was a successful night for Toffees manager Sean Dyche facing the team he served for nine-and-a-half years for the first time.
It was also further evidence of the progress being made at L4, with the home side now winning five of their previous seven games in all competitions.
Everton started the game on top, with Dominic Calvert-Lewin heading wide in the ninth minute before Onana’s low drive was well held by Burnley keeper Arijanet Muric.
And the deadlock was broken in the 13th minute when the two ex-Clarets combined. McNeil whipped in a cross from the left that picked out Tarkowski to power home a header. Then six minutes later, McNeil almost condemned his previous employers to fall further behind but his 25-yard shot missed the target.
Jordan Pickford was barely troubled in the Blues goal throughout the opening 45 minutes, with Jarrad Branthwaite making two important blocks to quell promising Burnley moves. On 29 minutes, Onana was left to rue a good opportunity when Muric spilled a cross but the Belgium international failed to finish into an unguarded goal.
Early in the second half, Calvert-Lewin had the ball in the back of the net but was penalised for a foul in the build-up. The striker then won Everton a corner, which would deliver a two-goal advantage. McNeil’s inviting cross was headed across the box by Tarkowski and there was Onana on hand to prod home from close range.
In the 64 minute, the Toffees should have put the game to bed. Calvert-Lewin span away from the Burnley defence wonderfully and Danjuma raced clear inside the box unmarked - but just couldn’t be found.
Dyche’s troops remained relatively comfortable for the rest of the encounter and looked far more likely to augment their advantage rather than see it decrease. Substitute Beto was disappointed he couldn’t find the target when he found space from six yards while Young forced a decent save out of Muric. But Young would notch his maiden Everton goal in stoppage-time when Beto pulled a cross from the byline and the former Aston Villa man steered beyond the keeper.
All in all, it was a thoroughly deserved win for an upwardly mobile Blues side who are now three games from a Wembley appearance. Here’s how we rated the Everton players.