Nam Ki-il's men recorded a 3-1 win in the first leg at home, and the draw at the Changwon Football Center was enough to seal their place in the top flight on Saturday.
Gyeongnam, who finished in the K-League relegation play-off spot, had been given hope of coming from behind.
Song Su-young netted a 71st-minute goal at home to put them within reach of an unlikely aggregate win.
But, just four minutes later, Kim Ho-nam levelled for the visitors – and there would be no way back for Gyeongnam.
Cho Yong-tae, Diego Silva and Sreten Sretenovic had scored in the important first-leg victory.
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