The tie was effectively settled in the opening 24 minutes as the Toffees powered ahead at the KC Stadium with goals from Ayegbeni Yakubu, Jo and Dan Gosling. David Moyes' men, finding their form after a poor start to the season, then eased off but took their goal tally to 11 in three games as Leon Osman added a fourth after 57 minutes.
Elsewhere in the Carling Cup, Peter Crouch's hat-trick helped Tottenham beat Preston 5-1, Chelsea beat QPR 1-0, while Aston Villa beat Cardiff by the same scoreline.
Spurs boss Harry Redknapp made seven changes for the third-round tie and Crouch emerged as the prime beneficiary as his predatory strikes took his season tally to five.
Crouch made the most of his recall in the 14th minute when he dispatched Gareth Bale's deep cross with a fine volley and Jermain Defoe effectively put Preston to bed with a predatory header seven minutes before half-time.
With 13 minutes remaining, Crouch tapped home Aaron Lennon's low cross before Preston pulled a goal back in the 83rd minute through substitute Chris Brown, only for Spurs substitute Robbie Keane to add a fourth and Crouch cheekily completed his hat-trick in injury time.
At Stamford Bridge Chelsea midfielder Joe Cole returned from his long-term knee injury to help defeat QPR 1-0 and send the Barclays Premier League leaders through.
The 27-year-old, named by manager Carlo Ancelotti as skipper for the evening, was playing in his first match since January and set up Salomon Kalou's winner at Stamford Bridge.
Meanwhile, Gabriel Agbonlahor ensured Aston Villa avoided more Carling Cup humiliation with his third-minute goal sufficient to overcome Cardiff at Villa Park.
Villa had crashed out of the competition to lower-league opposition in three of the previous four seasons, but Agbonlahor continued his hot scoring streak after linking up with fellow striker John Carew to ensure James Milner's missed penalty would not cost them.