With the Bluewings struggling in mid-table in the K-League, cup success represents their best home of success and qualification for the 2012 AFC Champions League.
Lee's strike made the difference, as he fired home a long-range shot after 25 minutes of the match at Suwon World Cup Stadium.
Defending AFC Champions League holders Seongnam Ilhwa defeated Busan I'Park 2-1, with Dzenan Radoncic returning from injury to score the winner in the last minute. Han Sang-woon of Busan had cancelled out an early strike by Heverton.
Pohang Steelers beat K-League champions FC Seoul 4-2 after extra-time. Goals from Derek Asamoah, Mota and Noh Byung-joon, who scored twice in the additional 30 minutes, proved too much for the visitors whose second-half efforts came from Dejan Damjanovic and Mauricio Molina.
Lee Sul-gi was the hero with a hat-trick for Ulsan Horang-I as they completed the last four line-up with a 3-0 win at home against Gangwon FC.