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Liverpool took the lead as Villa failed to clear the danger on the edge of their own box, with Jores Okore and Fabian Delph the guilty parties. Raheem Sterling slid a pass into the feet of Coutinho, who beat a couple of challenges before burying the ball into the back of the net with the aid of a deflection.
Villa's response was immediate as they drew level in the 36th minute. Delph atoned for his error with a mazy run down the left before exchanging a neat one-two with Jack Grealish to get into the area and cut the ball back into the middle for Benteke to fire past Mignolet.
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In the second half, Sherwood's men settled quickly back into their rhythm and took the lead when Benteke broke away down the left and found Grealish on the edge of the box. The youngster did well to pick out the run of Delph, who turned back inside and finished past Mignolet.
Alberto Moreno kept Liverpool in the game as he made a vital intervention to stop Benteke in his tracks as the Belgian attempted to collect a pass from Bacuna that would have sent him one-on-one with Mignolet.
The Reds had a chance to threaten when Coutinho was brought down just outside the box by Delph. Steven Gerrard stood over the ball and whipped his effort over the wall, but Shay Given was able to make a comfortable save to deny the Liverpool skipper.
Brendan Rodgers's side upped the ante late in the game as they threatened from two corners, but Dejan Lovren put his header over the bar while Gerrard's looping effort was cleared off the line by Kieran Richardson.
Liverpool continued to put the pressure on the Villans as Mario Balotelli headed narrowly over the bar in the dying minutes, but Sherwood's men held out to secure the victory to reach their first final since the 1999-00 season.