Kang's home run pulled South Korea even with Taiwan and the Netherlands at 2-1 after round-robin play but tiebreaking procedures advance Taiwan and the Netherlands, leaving South Korea out of the WBC second round.
Australia, the fourth Pool B team, wound up 0-3, including a 4-1 loss to the Netherlands earlier Tuesday.
Taiwanese pitching held South Korea to five hits over seven shutout innings but the Koreans reached reliever Kuo Hung-Chih (0-1) for three runs on three hits in the eighth.
Lee Seung-yeop started the South Korean rally with a double and scored on Lee Dae-ho's base hit. Kuo got two outs but Kang lined an 0-2 pitch over the left-field wall for a two-run home run and 3-2 lead.
Jang Won-sam Jang (1-0), South Korea's fifth pitcher in the game, pitched the eighth inning in collecting the win. Oh Seung-hwan Oh needed just seven pitches to get the final three outs and the save.
Yang Dai-kang scored a run in the third inning and knocked in one in the fourth to account for the South Korean scoring.
Ray Liotta sues skin care company over use of likeness
Millions of Getty images now available for free via embed tool