The Toffees have seen off Chelsea, Arsenal and Manchester United on their patch recently - by an aggregate score of 7-0 - and two goals in three first-half minutes proved decisive against the Clarets.
Burnley defender Ben Mee got a telling final touch to Richarlison's strike while Seamus Coleman headed in on the rebound as Everton ran out 2-0 winners in both sides' penultimate fixture of the campaign.
The win moved Everton up to eighth and to within a single point of Wolves in seventh - a position that will seal a Europa League berth next season if Manchester City beat Watford in the FA Cup final later this month.