Verdasco, who beat Britain's Andy Murray in the previous round, made a confident start against Nishioka, but the Japanese fought back to win 1-6 6-3 7-6(5) to reach the first ATP Tour final of his career.
Nishioka, who lost to Verdasco at this year's French Open, roared back after tamely surrendering the opening set and kept his wits about him in the tiebreak to wrap up his first career victory over the Spaniard in two hours 20 minutes.
Herbert is better known for his skill as a doubles player, but reached his second career ATP World Tour final after surviving a De Minaur fightback in the second set.
The Australian clawed his back from 3-0 down in the final set to force the tiebreak and even had two chances to win the match, but Herbert was equal to the task.
The Frenchman saved the first match point with a volley under pressure and shut out De Minaur a second time with an overhead smash before sealing victory with his 42nd winner of the contest.
(Reporting by Simon Jennings in Bengaluru; editing by Clare Fallon)
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