The Mariners battled heroically throughout the game at Mariners Park to force extra-time and penalties.
Julio Arca was also sent off in the second half of extra-time in extremely controversial circumstances.
When the game went to penalties, Aycliffe came out on top 3-1 as Shields lost a shoot-out for the second time this season, having lost in the FA Vase to Morpeth by the same method.
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The hosts started well against their Northern League Division One opponents, and were handed a great chance to take the lead when David Foley was brought down in the box.
Arca stepped up and coolly sent the goalkeeper the wrong way from the spot for his ninth goal of the season.
Aycliffe responded well, and had the better of the rest of the first half.
After an earlier warning as to his quality from set pieces, Dennis Knight struck with a stunning free-kick from the left which arrowed in off the post.
The Mariners came through a difficult spell after that, with the visitors attacking well, while Lewis Teasdale and Robert Briggs were denied at the other end.
Aycliffe took the lead in the second half with a stunning strike by Zak Boagey from 30 yards, but Shields came back excellently.
They penned their opponents back before equalising nine minutes before the end when Briggs’ brilliant corner from the left was headed in by Michael Turner.
The crowd of 517 was right behind the Mariners, cheering every tackle as they pushed for a winner.
However, it did not arrive, and the game went into extra-time.
Scott Pocklington made terrific saves from Stuart Banks and John Campbell, while Arca headed just wide at the other end.
On 112 minutes came the most controversial moment when Arca appeared to be held to the ground several times by Neil Pattinson before forcing himself away.
The referee saw Arca’s actions as violent conduct and produced a red card, much to the disgust of the player and crowd.
Shields held out until penalties, but misses from Leepaul Scroggins, Warren Byrne and Robert Briggs proved pivotal as Aycliffe progressed to the final.
SOUTH SHIELDS: Pocklington, Hassan (Byrne 120), Grey (Ramsey 77), Hall, Turner, Arca, Foley, Scroggins (c), Coleman, Teasdale (Phillips 64), Briggs. Sub not used: Young.
Goals: Arca (pen 17), Turner (81).
Red card: Arca (112).