World number five Nishikori will seek his eighth ATP title when he meets second seed Kevin Anderson in the final on Sunday.
The South African also dropped the first set before recovering to beat American Donald Young 4-6 6-3 6-4.
Anderson, 28, staved off four break points in the second and third sets to triumph in just under two hours.
Nishikori had trouble against Querrey's serve and in the end was mightily relieved to edge the world number 41.
Last year's U.S. Open finalist trailed 2-4 in the final set tiebreaker, before winning five of the next six points to scrape through.
"I thought a couple times that I might lose," Nishikori told reporters. "I knew it was going to be tough because I didn't break any of his serves... It was really tough to make any returns."
Nishikori, 25, has lost the first set in all three of his matches this week.
"I'm a little bit tired from playing three tough matches, but it's just one more match," he said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Patrick Johnston/Sudipto Ganguly)
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