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Nottingham Forest took an early lead through Brennan Johnson, to go 3-1 up on aggregate and take command of the tie.
Second half goals to Morgan Gibbs-White and John Fleck sent an incident-packed encounter to extra time, where Samba's stunning save to deny Gibbs-White from in front was the decisive moment.
The Keeper then saved United's first two penalties in the shootout, before denying Gibbs-White again, from the spot, to send Forest into the EFL play-off championship final, against Huddersfield at Wembley.
