The Black Cats had won 2-1 at the Stadium of Light a fortnight ago and managed to hold on despite losing 2-1 at Old Trafford in the return leg.
That set up a penalty shootout at the Theatre of Dreams which turned out beautifully for the visitors who edged their more fancied rivals 2-1 in a period dominated by the goalkeepers.
In the 37th minute, Jonny Evans reduced United's deficit when he headed home a Danny Welbeck flick-on from a corner but neither side could find a winner which led to extra-time with the aggregate at 2-2.
In the 119th minute of the contest, Phil Bardsley attempted a goalbound effort from the edge of the area which United keeper David de Gea somehow let through in what was a massive blunder.
That sent the match into penalties and it was a dour struggle for the spot-kick takers with only three of the ten men converting from 12 yards.
For Sunderland, Craig Gardner skied, Steven Fletcher was denied by de Gea and Adam Johnson sprayed his effort while United's Welbeck, Januzaj, Phil Jones and Rafael all missed with the latter seeing his effort saved by Black Cats keeper Vito Mannone which sent the Wearside club through.
Gus Poyet's Sunderland, who had 9,000 travelling fans in full voice, will now take on the in-form Manchester City, who beat West Ham United 9-0 on aggregate, in the Capital One Cup final at Wembley on March 2.
2013/14 Capital One Cup semi-final - second leg
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