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.