Elliot Embleton opened the scoring for Alex Neil’s side in the 12th minute with a long-range strike which was too powerful for goalkeeper David Stockdale.
During a tense second half, Sunderland goalkeeper Anothey Patterson also made some important interventions - most notably to deny striker Sam Vokes.
Ross Stewart then doubled his side’s lead ten minutes from time after he was set up by Alex Pritchard.
Our chief SAFC writer Phil Smith has delivered his verdict on how each Black Cats player fared at Wembley:
1. Anthony Patterson - 9
The maturity with which he handled the occasion was quite remarkable. Claimed crosses, dominated his box, used the ball well and stood tall on the one occasion his team really needed him. What a rise. 9 Photo: JPI Media
2. Lynden Gooch - 8
Another tenacious performance out of position. The kind of selfless approach that has hauled the Black Cats over the line. What a moment for a player who has given it everything for his club for years. 8 Photo: Frank Reid
3. Danny Batth - 9
A domineering display at the heart of the defence. Made countless blocks, won his headers and never made an error on the ball. He has been integral to this late surge to promotion. 9 Photo: JPI Media
4. Bailey Wright - 8
Made one misjudgement in the second half but his goalkeeper was there to make the save. Outstanding otherwise, superb in his duel against the dangerous Vokes. 8 Photo: JPI Media