Gary Caldwell fired a shot well over at the other end, before Yoo Sang-Chul twice threatened the Scots goal.
But the inevitable second goal arrived in the 58th minute from substitute Ahn Jung-Hwan.
He turned Alexander inside out and fired a 20-yard shot past Sullivan, who might have made a better fist of his attempt at saving the effort.
Yoon Jong-Hwan, marked his entry in astonishing fashion by hammering a remarkable third goal past Sullivan from long range.
Scotland were given something to shout about when debutant Dobie headed a consolation goal in the 74th minute, meeting a Scot Gemmill free kick at the back post.
But the South Koreans were not yet finished and they rounded things off with a fantastic fourth goal.
Perugia striker Ahn Jung-Hwan rounded off a superb move with a delicate chip over Sullivan.
South Korea: Kim Byung-Ji, Hong Myung-Bo, Yoo Sang-Chul, Choi Jin-Chul, Kim Tae-Young, Song Chong-Gug, Lee Eul-Yong, Park Ji-Sung, Lee Young-Pyo, Lee Chun-Soo, Hwang Sun-Hong. Subs: Lee Woon-Jae, Choi Eun-Sung, Lee Min-Sung, Kim Nam-Il, Choi Sung-Yong, Hyun Young-Min, Yoon Jong-Hwan, Ahn Jung-Hwan, Seol Ki-Hyeon, Choi Yong-Soo, Cha Doo-Ri, Choi Tae-Uk.
Scotland: Sullivan, Graham Alexander, Dailly, Weir, Ross,
Gary Caldwell, Gemmill, Stewart, Johnston, Dobie, O'Connor.
Subs: Paul Gallacher, Neil Alexander, Stockdale, Wilkie,
Cummings, Severin, Williams, McFadden, Kyle.
Referee: N Sanghan (Singapore).