The Belgian striker netted twice as David Moyes' men booked their place in the third round of the League Cup with an emphatic win over their League One opponents
New summer signing Kevin Mirallas opened the scoring 15 minutes into the contest, before Leon Osman doubled the tally six minutes later.
Mirallas then netted again just before the half-hour mark, and Victor Anichebe rounded off a first half rout 10 minutes before the half-time interval.
Despite their lead, the Toffees refused to slow down after the break, and Frenchman Magaye Gueye added a fifth midway through the second half.
David Moyes' men started quickly and dominated the early going with Mirallas and Anichebe both troubling the Orient defence on multiple occasions in the opening ten minutes.
And it was the Belgian Mirallas who broke the deadlock, as he fired a left-footed strike into the bottom corner of the net from close range to give the home side the lead.
Their advantage was quickly doubled, Mirallas involved again as he played in Osman to fire past Orient keeper Jamie Jones from just inside the area.
Mirallas, who was making his home debut for the Toffees, continued to be at the forefront of Everton's attacking play and he soon added a third, firing home a right-footed effort to put the result beyond any doubt.
Everton refused to relax despite their healthy advantage and, shortly after Leighton Baines had an effort brilliantly saved by Jones, they duly notched their fourth, Anichebe finding the net with a fierce drive from just outside the area.
Orient were given brief respite as the half-time interval arrived, and their performance did improve slightly in the opening exchanges of the second period, with striker Kevin Lisbie denied a consolation goal 10 minutes in thanks to a good save from Jan Mucha.
The evening undoubtedly belonged to Everton however, and they put the gloss on a highly professional display when Gueye wrapped up the victory with a superb strike, the French midfielder powering home from 20 yards to cap a very satisfactory night for Moyes' men.