It is the penultimate competition of the year for Murray, who has chose to play in the Shenzhen and China Opens before ending his season in order to work on improving the hip issue that has troubled his recent career.
Fifth seed Verdasco defeated the former world number one 6-4 6-4 to reach the semi-finals.
Murray next plays the man who knocked him out of the US Open, Spain's Fernando Verdasco. "There weren't many opportunities there, but the first set I had some chances".More news: Kanye West Attempts To Clarify 13th Amendment Comments, Chris Evans Roasts Him
Murray broke the defending champion's serve five times and saved seven of 10 break points.
The 31-year-old has seen his world ranking drop to 311 due to the persistent hip problems that necessitated surgery.
Murray, a three-time Grand Slam victor, has slipped to 311th in the world as a result of his lay-off.More news: Tweet storm: Musk quits as chairman over false claims
After losing in the quarter-finals of the Shenzhen Open, Murray decided that it was best not to play his scheduled final tournament of the year. "Right now, I feel like as the week goes on, I'm slowing down a little bit".
Experienced Spaniard Verdasco dominated the first set, but was left stunned after Nishioka came storming back to set up an unlikely Sunday showdown.
Pierre-Hugues Herbert takes on Alex de Minaur of Australia in the other semi, after the Frenchman took just under three hours to overcome Albert Ramos-Vinolas 6-7 (4) 7-6 (3) 6-4.More news: Dominant Juventus now Europe's best with Cristiano - Inzaghi
He should get exactly that against the 27-year-old Herbert, a three-time Grand Slam doubles title victor.