Belgian Kevin Mirallas and Leighton Baines put the home side 2-0 up in the first half before Leon Osman added a third after the hour mark to show the gulf in class against Liverpool's surprise fourth-round conquerors.
Matt Smith, who equalised in the last minute for Oldham in the 2-2 draw at home to Everton on Feb. 16, struck with a header from a corner moments later to give the visitors hope but the hosts were never really troubled again in the final half hour.
Everton will next host Wigan on March 9 (1245 GMT).
