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Midfielder Ilia Gruev gave Leeds the lead in the seventh minute, scoring his first goal for the club, before Joel Piroe and Georginio Rutter put the hosts 3-0 up at the break. Crysencio Summerville added the fourth in the second half.
The sides played out a goalless draw in the first leg on Sunday.
Southampton and West Bromwich Albion face each other on Friday in the second leg of the other semifinal, also following a 0-0 draw.
The final will be played on May 26 at Wembley.
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