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.
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.
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.
"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."
