An inspired second-half performance from the Blades was enough to force extra time after they fell behind in the first period thanks to Brennan Johnson’s goal, but Forest goalkeeper Brice Samba saved three penalties in the shootout to send his side to Wembley.
Goals from Morgan Gibbs-White and John Fleck gave Paul Heckingbottom’s side a 2-1 win on the night, which levelled the scores at 3-3 overall.
Samba saved from Ollie Norwood, Conor Hourihane and Gibbs-White, with Sander Berge and Iliman Ndiaye converting their spot kicks.
Brennan Johnson, Steve Cook and Cafu scored for the home side, but Joe Lolley blazed his effort over the bar.
Scroll down for our player ratings.
. Sheffield United player ratings
Morgan Gibbs-White celebrates his goal with teammate Iliman Ndiaye. Photo: Simon Bellis
. Wes Foderingham - 7
No chance with the goal and made a smart stop to deny Davis from close range in extra time. Photo: Isaac Parkin
. Chris Basham - 6
Generally solid and unruffled. Made a brilliant block to prevent a goal-scoring opportunity for Forest before making another surging run from deep to drive United forward. Photo: David Klein
. Rhys Norrington-Davies - 6
Did a better job than Stevens of keeping Spence quiet, though the opening goal did come from his side. Photo: Andrew Yates
1. Sheffield United player ratings
Morgan Gibbs-White celebrates his goal with teammate Iliman Ndiaye. Photo: Simon Bellis
2. Wes Foderingham - 7
No chance with the goal and made a smart stop to deny Davis from close range in extra time. Photo: Isaac Parkin
3. Chris Basham - 6
Generally solid and unruffled. Made a brilliant block to prevent a goal-scoring opportunity for Forest before making another surging run from deep to drive United forward. Photo: David Klein
4. Rhys Norrington-Davies - 6
Did a better job than Stevens of keeping Spence quiet, though the opening goal did come from his side. Photo: Andrew Yates