The scoreline flattered last season's runners-up, whose place in the fourth round was not assured until Leighton Baines converted a penalty deep into stoppage time after their League One opponents had surprised a Goodison crowd primed for a stroll with some good quality football that deserved better luck.
The Cumbrians, cheered on by 6,000 fans despite bad weather hampering their journey along the M6, matched the Premier League side almost throughout and the manager Greg Abbott's claim that a kinder rub of the green might have seen them celebrating a shock victory was by no means fanciful, given that Everton had benefited from a Carlisle mistake for their opening goal and, arguably, a linesman's error for their second.
It was a claim with which even David Moyes, the Everton manager, had sympathy, having seen James Vaughan take advantage of a sloppy backpass to put the home side in front after 12 minutes and then watched Tim Cahill restore their lead with eight minutes left after the substitute Seamus Coleman had been allowed to play on and cross despite appearing to foul Carlisle's Matt Robson.
"We feel there was a foul in the build-up to Everton's second goal and though we don't like to complain about the officials that was a big decision that ultimately cost us the game," Abbott said.
"But I'm proud of the way we played. There was never a gulf between the sides and with a little bit more of a rub of the green we might have been sitting here talking about a draw or even a shock victory.
"David Moyes spoke to me at the end and said he thought we were very unlucky."
Kevan Hurst had scored Carlisle's goal six minutes after Everton had taken the lead. They were denied a second after 71 minutes when the Everton goalkeeper Tim Howard touched a Danny Livesey volley on to the bar.
"Carlisle were always a threat and did their supporters proud but you would not expect anything different in the Cup," Moyes said, relieved to have avoided Everton's third-round fate two seasons ago, when they lost to Oldham of League One. "But for a wonder save by Tim and the ball hitting the bar it might have been a different story."
Moyes had been respectful enough of Carlisle's seven-game unbeaten run to field a strong line-up, showing only two changes. Having suspended the Brazilian Jo and with Louis Saha injured, he introduced James Vaughan in place of the unavailable Ayegbeni Yakubu for a first start of the season and recalled his captain, Phil Neville, who was starting for the first time since mid-September following injury.
When Vaughan fired Everton ahead after 12 minutes, their passage looked likely to be straightforward, even if it had taken an error by the otherwise impressive Adam Clayton, whose backpass the striker intercepted, to create the opportunity. Vaughan, scoring for the second time in a week after his long recovery from knee problems, glided past goalkeeper Adam Collin to slide the ball into an empty net.
But the Cumbrians were unfazed and it took them barely six minutes to correct Clayton's error. A well- crafted move along the left created a chance for Clayton to repair the damage himself when Vincent Pericard, the former Portsmouth front man, flicked the ball into his path. Clayton, on loan from Manchester City, saw his own shot strike Howard but Hurst was on hand to force the ball across the line.
Clayton, 20, alongside 19-year-old Tom Taiwo, on loan from Chelsea, were outstanding in central midfield and there were impressive contributions also from Robson and Ian Harte, the former Leeds defender, who brought authority to their defence.
Their resistance cracked only when Coleman's shove on Robson went unpunished and his cross allowed Cahill to stab home before Collin brought down substitute Kieran Agard to condede the penalty.
Referee: Jon Moss
Man of the match: Taiwo
Match rating: 7/10