The Toffees made a flying start despite the sweltering conditions and they were 2-0 up after 16 minutes thanks to goals from Victor Anichebe and Diniyar Bilyaletdinov.
Anichebe raced onto a throughball from Leighton Baines and finished from an acute angle in the fourth minute.
Bilyaletdinov then followed up with a calm finish after a superb move which involved Jack Rodwell, Ross Barkley and Apostolos Vellios.
Chris Pontius pulled a goal back shortly after the restart when he beat Jan Mucha from Dwayne De Rosario's pass.
But Magaye Gueye wrapped up the win for Everton on 81 when he slotted home Jermaine Beckford's cross.
Boss David Moyes told the club's website: "I was quite pleased we got the result. I thought it was a good game.
"They had a few chances as well. The conditions played a part and all credit to both teams for making it as entertaining as they could."