Uruguayan Suarez, banned earlier this season after racially insulting Manchester United's full-back Patrice Evra, scored Liverpool's equaliser to put his side back in the game following a mistake by Everton's Sylvain Distin after 62 minutes.
Carroll, who has been roundly criticised for his lack of goals since his British record 35 million-pound transfer from Newcastle United last year, headed the winner three minutes from time.
He had earlier missed easier chances, the first just after half-time when he headed wide two metres from goal, but he told ESPN that scoring the winner was "the best feeling ever".
The 23-year-old Geordie added: "It's a great feeling. I've had some criticism but I've kept on going. I've got the winner here and I believe in myself every day."
Suarez's equaliser and Carroll's winner ripped the heart out of an Everton side who deservedly went ahead with a 24th minute strike from their Croatia forward Nikica Jelavic.
Both Jelavic's goal and Suarez's strike came after defensive errors with Jelavic benefiting from a mix-up between Jamie Carragher and Daniel Agger who failed to clear a loose ball.
Suarez struck after Distin underhit a back-pass into his path. That mistake by the Frenchman changed the course of the game.
Liverpool, who had played poorly until then, gradually took control after Suarez's goal and in the end just about deserved to reach their first FA Cup final since 2006.
The game looked to be heading into extra time when Everton substitute Seamus Coleman needlessly fouled Liverpool skipper Steven Gerrard to concede a free-kick wide on the left.
Craig Bellamy, who had only been on the pitch for a few minutes, whipped in a perfect cross which Carroll glanced past the despairing Everton goalkeeper Tim Howard.
While Suarez and Carroll have had their personal difficulties, Liverpool generally have underperformed in the Premier League, and their owners acted to change that this week when they dismissed the club's director of football.
Daniel Comolli left the club as a result of the perceived failure of his transfer policy - which included the expensive acquisitions of Suarez and Carroll.
Liverpool manager Kenny Dalglish, who said on Friday he had a good working relationship with Comolli, believed his side deserved to reach their second final of the season after winning the League Cup against Cardiff City in February.
"The players who were out there and those who have made a contribution through the run, have been fantastic, their application was there for everyone to see," he told reporters.
"Everything you need to win a game of football we showed today as a team.
"It was fantastic, it has not been too good over the last few weeks but that's two cup finals, one we've won and one we're looking forward to. It gives everyone a lift. We're very proud and pleased."
He refused to single out Carro
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