Luton started confidently enough in this Carling Cup third round tie, but in Mikel Arteta, Tim Cahill and Andy Johnson, Everton looked to have the edge with the Australia international midfielder almost heading in after 16 minutes.
A fine Arteta cross to Leon Osman almost broke the deadlock, but keeper Marlon Beresford was equal to the header.
Minutes later Arteta floated in a fine free-kick for acting left-back Joleon Lescott to rise and head across goal for a stooping Cahill to put the Toffees ahead.
Warren Feeney could have equalised for Luton against the run of play though as a defensive mix up allowed him a speculative overhead kick which rose above Iain Turner's crossbar.
Everton were two up on 34 minutes after a great tenacious run by Johnson. The lightening quick striker evaded Kevin Foley before providing a hard, low cross that Keith Keane, with James McFadden bearing down on him, couldn't help but put past his own keeper.
Keane was the culprit again as he brought Johnson down in his own area, but Arteta tamely shot straight at Beresford.
David Weir was knocked unconscious after colliding with Leon Barnett after Dean Morgan had hit the post for Luton. He left the pitch on a stretcher and in a neck brace to a standing ovation.
After the interval Everton carried on were they left off as McFadden then Arteta then Alan Stubbs almost made it three in the first minute after the restart.
McFadden made it three on 53 minutes after Arteta had played in Cahill to cross for the Scot as Everton threatened to run riot.
Arteta played a perfect ball through to Johnson but the over-confident striker took too long to get his shot off and Beresford collected gratefully.
Beresford kept the score down with a fantastic save from McFadden's header and Arteta hit the post as the tie started to look like men against boys.
Everton laid siege to the Luton goal and Hatters boss Mike Newell must have been wishing he had stayed at home.
Victor Anichebe came off the bench and promptly made it four to wrap the game up.
The youngster showed great composure to slide his left-foot effort into the bottom corner after shrugging off Foley.