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.
Samba saved from Ollie Norwood, Conor Hourihane and Gibbs-White, with Sander Berge and Iliman Ndiaye converting their spot kicks.