John Fleck and Almond blasted efforts wide of Lindegaard's goal while United responded with a Brady scooped shot that was easily handled by Halstead and another wayward drive from the Irishman when Rudge was in the clear to his left.
Lindegaard denied Almond in stoppage time so the tie went to a penalty shoot-out and the Scandinavian shot-stopper kept out Blackpool's first kick by Robert Harris. Although King, Reece Brown, Luke Giverin and Brady scored, Scott Wootton's miss meant sudden death.
Ekangamene displayed great composure to chip his spot-kick over Halstead and substitute Menagh showed courage to face Lindegaard from 12 yards but the Dane's save means United progress to the final against Accrington Stanley, with the pre-season date to still be confirmed.
United: Lindegaard; Vermijl, Wootton, Brown, Giverin; Rudge (Gorre 89), Fornasier, Hendrie, Ekangamene, Brady; King. Subs: Wilkinson, Johnstone, Fletcher.