Odion Ighalo broke the deadlock six minutes into the second half when he fired the ball past Canaries stopper Tim Krul from close range, but Todd Cantwell levelled things up for the hosts with a strike from the edge of the area, 15 minutes from time.
Despite being reduced to 10 men when Ighalo was pulled down by Timm Klose, Norwich managed to hang on in the closing stages and force the game into extra-time. With penalties on the cards, the ball broke to Maguire, who was still in the box following a corner, and the United captain took his chance to send the Reds to Wembley.