Match ends, Carlisle United 0, Everton 3.
Arouna Kone, Aaron Lennon and Ross Barkley scored as Everton progressed to the fifth round of the FA Cup with a comfortable victory at Carlisle.
Everton took the lead inside two minutes when a ball from Tom Cleverley released Lennon down the right and he crossed low for Kone to tap in.
Lennon effectively ended hopes of an upset when he received Bryan Oviedo's centre and squeezed in an angled shot.
And Barkley's deflected long-range effort capped an assured display.
The 1995 winners will now travel to take on Bournemouth in the fifth round.
League Two Carlisle's best chance came at 1-0 down when Derek Asamoah fired straight at Joel Robles.
The Cumbrians' exit means there are now no sides from outside the top three divisions remaining in the FA Cup.
Everton meanwhile continue their strong recent record in the FA Cup and will be in the fifth-round draw for the fifth time in the last six seasons.
Toffees bounce back from League Cup disappointment
Everton surrendered a first-leg lead in losing to Manchester City in the League Cup semi-final on Tuesday, and manager Roberto Martinez has come under pressure this season after a series of underwhelming results.
But the Spaniard is well aware of the importance of the FA Cup - having won the competition with Wigan in 2013 - and he named a strong side, with Phil Jagielka, Ramiro Funes Mori, Cleverly and Barkley all retained from that midweek defeat.
Cleverley in particular was outstanding, having more touches than anyone else on the pitch and finding the target with 95% of his passes.
And despite the lowly calibre of the opposition, this was the kind of display that will give Martinez hope that his side can add to their six league wins and finish the season strongly.
Carlisle's big day falls flat
Much effort had gone in to making sure the pitch at Brunton Park was playable after the stadium was flooded during Storm Desmond.
But while the newly-laid surface held firm, Keith Curle's side were swamped by Everton's pace and verve in attacking areas.
The hosts had just 29.7% of possession and only managed two shots on target.
Their attentions now turn to making a late push for the League Two play-off places.
Man of the match - Aaron Lennon
What they said
Carlisle manager Keith Curle: "It wasn't ideal with the two early goals, very quickly you are on to plan B. We knew how good they were and wanted to try and contain them for as long as possible.
"Two down after 14 minutes you know it was going to be a long afternoon. Credit for the players to the way they responded.
"It was a fantastic experience for our players. We got turned over by a fantastic team. A lot of praise has to go to everybody, hopefully we have done a lot of people proud."
Everton manager Roberto Martinez: "We knew that you can allow these games to be very complicated. I thought we dealt with it with an incredible professionalism. The start of the game allowed us to control the rest of it.
"The fourth round of the FA Cup always brings excitement. I thought we played well and controlled the threat that Carlisle can bring. We scored three goals, created chances and overall we deserved it and look forward to a draw."
The stats you need to know
- Arouna Kone has scored four goals in six FA Cup appearances for Wigan and Everton.
- Kone's goal after 91 seconds was the second quickest goal in the FA Cup this season, with only Newport's Lennell John-Lewis scoring faster (36 seconds).
- Ross Barkley has scored in back to back games after failing to score in his 11 previous games.
- Everton have progressed in their last nine FA Cup ties against lower league opposition, scoring 29 goals in the process and conceding just five.
Carlisle face Accrington in League Two on Saturday, while Everton host Newcastle in the Premier League on Wednesday evening.
- 15ComleySubstituted forIbehreat 63'minutes
- 16DickerSubstituted forGillieadat 45'minutes
- 26GillespheySubstituted forHopeat 45'minutes
- 7KennedyBooked at 48mins
- 23ColemanSubstituted forGallowayat 83'minutes
- 25Funes Mori
- 16McCarthyBooked at 44mins
- 20BarkleySubstituted forGibsonat 75'minutes
- 22PienaarSubstituted forOsmanat 62'minutes
- Lee Mason
- Shots on Target
Second Half ends, Carlisle United 0, Everton 3.
Bryan Oviedo (Everton) wins a free kick in the defensive half.
Foul by Hallam Hope (Carlisle United).
Foul by Ramiro Funes Mori (Everton).
Tom Miller (Carlisle United) wins a free kick in the attacking half.
Attempt saved. Darron Gibson (Everton) right footed shot from outside the box is saved in the centre of the goal. Assisted by Aaron Lennon.
Foul by Darron Gibson (Everton).
Hallam Hope (Carlisle United) wins a free kick in the attacking half.
Attempt blocked. Jabo Ibehre (Carlisle United) right footed shot from the centre of the box is blocked. Assisted by Alex Gilliead.
Attempt blocked. Bryan Oviedo (Everton) left footed shot from the right side of the box is blocked. Assisted by Leon Osman.
Corner, Carlisle United. Conceded by Bryan Oviedo.
Attempt saved. Antony Sweeney (Carlisle United) left footed shot from the left side of the six yard box is saved in the centre of the goal.
Substitution, Everton. Brendan Galloway replaces Seamus Coleman.
Offside, Everton. Leon Osman tries a through ball, but Arouna Koné is caught offside.
Attempt missed. Leon Osman (Everton) left footed shot from outside the box misses to the left. Assisted by Seamus Coleman.
Attempt missed. Seamus Coleman (Everton) right footed shot from outside the box is too high. Assisted by James McCarthy.
Phil Jagielka (Everton) wins a free kick on the right wing.
Foul by Jabo Ibehre (Carlisle United).
Substitution, Everton. Darron Gibson replaces Ross Barkley.