Roberto Martinez opted to rest John Stones, Gerard Deulofeu and Romelu Lukaku, but his side never looked likely to suffer an upset against a team lying in mid-table in England's fourth tier.
Aaron Lennon teed up Arouna Kone to open the scoring with just two minutes on the clock and the former Tottenham winger doubled the lead inside the first quarter of an hour.
Everton fans had contributed to the restoration of Brunton Park, which was hugely affected by the December storms in the UK, and they had plenty to enjoy about their journey north as Ross Barkley drilled in a deflected third after the break.
Carlisle had lost all three previous FA Cup ties with the Merseysiders and rarely looked likely to spring a shock, with Derek Asamoah coming closest to finding a way past Joel Robles in what proved to be a frustrating outing for the hosts, as Everton marched into round five for the fifth time in six seasons with a result that will go some way towards banishing memories of their League Cup semi-final heartbreak against Manchester City.
The home fans - who numbered more than 17,000 - were in fine voice as they welcomed Carlisle for their second game back on the relaid turf, but it took Everton just two minutes to strike the first blow.
Lennon burst into the box from the right and squared the ball across goal for Kone, who tapped home from close range.
Asamoah drew a strong stop from Robles with a half-volley at the near post but Lennon finished a fine team move to put the visitors in complete control with just 14 minutes played.
Bryan Oviedo combined superbly with Barkley before picking out the England international, who took a touch past Michael Raynes and slotted through Mark Gillespie's legs.
Carlisle created little to threaten Everton's advantage before the break and Keith Curle made two changes at half-time in an effort to galvanise his side - Asamoah coming closest to grabbing a lifeline as he fired narrowly over following Hallam Hope's long ball.
But Barkley ended any prospect of a shock comeback just past the hour mark. Striding into space on the edge of the area after Leon Osman's pass, his firm strike glanced off the head of Mark Ellis before nestling high into the net past the wrong-footed Gillespie.
Carlisle pushed for a late consolation, with Robles saving low to deny Antony Sweeney, but Everton comfortably saw out the closing stages to book their place in Sunday's fifth-round draw.