The Toffees started brightly and took the lead on 17 minutes when Richarlison's 25-yard shot deflected in off the knee of Ben Mee.
Seamus Coleman then headed in a second goal just three minutes later after Tom Heaton parried Lucas Digne's swerving shot into the Irishman's way.
Burnley improved after the interval as Johann Berg Gudmundsson weighed in with an effort, while Matej Vydra arguably could have been awarded a penalty after being shoved by Michael Keane.
Nonetheless, the Toffees were able to see the game out with little trouble against their opponents, who have already secured their spot in the Premier League for next season.
One player who impressed for Marco Silva's side was Kurt Zouma, whose display in central defence was top class, such was his calmness and composure.
However, there are fears that it may have been the Chelsea loanee's last game in Everton colours at Goodison, especially given how the Blues are still waiting to hear from FIFA on their appeal against a two window transfer ban.
Zouma took to Twitter after the game and some Everton fans pleaded with him to consider joining the Merseyside club permanently:
Lad stay at Everton— Everton Aren't We (@EvertonArentWe) May 3, 2019
Never leave, Kurt!— Everton Blue Army (@EvertonBlueArmy) May 3, 2019
Please stay Kurt— Paul Robinson (@paulsharyn) May 3, 2019
Love you. Please don't go x— Marc (@Rochey1878) May 3, 2019
Lad stay forever— Simon J Villiers (@sjv_simon) May 3, 2019
You deserve us.— Eric Howell (@Eric_Howell) May 4, 2019
We deserve you.
You know what you need to do ....— Paul (@goodysonx74) May 4, 2019
Michael Keane said he'll do lots of crying if you go. So you have no choice.— Terry Owen (@terry77owen) May 4, 2019
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