The home side were woeful in defence but clinical in attack and they will take a slender advantage to Korea for the second leg in a fortnight's time, optimistic they can reach their first continental final.
Substitute Fisal Bin Sultan scored the match-winner two minutes from time, calmly rounding goalkeeper Jung Sung-ryong and netting after a neat through-ball from Abdoh Autef.
The Korean side, however, will be kicking themselves that they did not at least draw the match after they led three times only to drop too deep in the final 10 minutes.
Colombian forward Mauricio Molina put the South Koreans ahead after only three minutes in the King Fahd International Stadium, where Seongnam won their sole Asian continental title in 1996.
Uruguayan Juan Manuel Olivera equalised for the home side 12 minutes later when he lobbed home but the Koreans regained the advantage in the 26th minute when midfielder Jo Jae-chul fired a low shot past Waleed Abdullah in the Shabab goal.
The Saudis equalised again in the 57th minute when Jung failed to stop a Nasser Al Shamrani left foot shot at his near post despite getting a hand to the ball.
Molina then scored with a classy half-volley after being allowed too much space in the Shabab penalty area.
The Koreans missed chances to extend their lead before Olivera scored his second with five minutes left, stabbing home after Jung had parried his initial header.
Iran's Zobahan host Saudi's Al-Hilal in the first leg of the second semi-final on Wednesday.
