Patrick Roberts scored a dramatic stoppage-time equaliser to put the Black Cats 2-1 ahead on aggregate.
It came after Wednesday striker Lee Gregory levelled the score, and the match looked set to go to extra-time before Roberts’ late finish.
Sunderland will now face Wycombe Wanderers in the final at Wembley Stadium later this month.
Our chief SAFC writer Phil Smith has delivered his verdict on how each Black Cats player fared at Hillsborough:
1. Anthony Patterson - 6
Brought a welcome calm for the most part aside from one or two nervy moments from crosses. Couldn’t do anything about the goal. 6 Photo: JPI Media
2. Danny Batth - 8
Looked crestfallen after the equalising goal but deserved to be on the winning side over two legs, winning so many of his duels. 8 Photo: JPI Media
3. Bailey Wright - 9
Once again led from the front, conducting his post-match duties with blood all over his face. That summed up what he has brought to the side of late. 9 Photo: JPI Media
4. Dennis Cirkin - 8
Sheffield Wednesday targeted his flank from the off but he stood up to the task with another tenacious showing. Showing so much guts. 8 Photo: JPI Media