Nishioka, who will return to the ATP's top 50, eliminated No.5 seed Dan Evans in the first round and later No.1 seed Casper Ruud in the quarter-finals.
Meanwhile, Kovacevic made his main-draw bow on Tuesday (AEST), beating No.7 seed Miomir Kecmanovic, and continued a sensational run all the way to the last four.
The American threatened another upset on Sunday (AEDT), but Nishioka held his nerve to advance 6-3 4-6 6-3 in Seoul.
Now the Japanese will revert to the role of underdog on Monday (AEDT), with No.4 seed Denis Shapovalov his opponent in the championship match.
Nishioka has only one ATP Tour title to his name, and he will have his work cut out if he is to add to that against Shapovalov, who is yet to drop a set this week.
The Canadian continued that sequence with a 7-5 6-4 success against Jenson Brooksby in the first semi-final.