The left-back was a surprise name in the Black Cats’ starting line-up on Sunday having missed the last two months with a shoulder injury, but scored the only goal of the game in the 33rd minute.
Van Aanholt was one of six changes to the side beaten by Manchester City on New Year’s Day, while Leeds made seven changes from the team which lost to Derby in midweek.
The 1-0 scoreline was a repeat of the Wembley outcome 42 years ago, when the then second division Wearsiders defied the odds to beat the top-flight aristocrats in the final.
Gus Poyet’s side dominated the first half as the visitors attempted to soak up pressure, but the Yorkshiremen responded after the break in front of a travelling contingent of 5,200 among a crowd of 30,302 at the Stadium of Light.
Adryan and debutant Brian Montenegro both tested Costel Pantilimon inside the opening five minutes of the second half, but neither could find the finish to drag their team back into the game, although Liam Cooper went agonisingly close to snatching a replay at the death.
Emanuele Giaccherini was first to catch the eye on 12 minutes, forcing keeper Marco Silvestri to save at his near post after tricking his way past full-back Gaetano Berardi, with Ricky Alvarez’s shot from the resulting corner deflected onto the top of the crossbar.
Steven Fletcher looked certain to open the scoring eight minutes later when he slid in to meet Van Aanholt’s driven cross, but only succeeded in spooning the ball high over from close range.
The pressure finally told 12 minutes minutes before the break when Fletcher rolled the ball into Van Aanholt’s path and the Dutchman, making his return from a 10-game absence, smashed an unstoppable shot across Silvestri and in off the far post.
Having already lost Jack Rodwell to injury before the break – he was replaced by Sebastian Larsson – Poyet sent on Connor Wickham for Alvarez at the break, but it was Pantilimon who had to be at his best within seconds when he denied Adryan with his legs after the midfielder had been played in by Mirco Antenucci.
The Romanian was called upon once again four minutes later to beat away Montenegro’s shot, and Larsson was relieved to see referee Mike Dean award a free-kick rather than a penalty for his trip on full-back Charlie Taylor on the edge of the box seconds later.
The visitors kept going to the final whistle and very nearly got their reward in added time when Cooper met Luke Murphy’s cross, but was denied by the woodwork.