Serbian Djokovic, 12-times grand slam champion, made 29 unforced errors against the 15th seed and converted just two of nine break points.
He saved three match points before Bautista Agut broke his serve for the fourth time to wrap up victory in one hour 48 minutes.
Djokovic, who smashed his racket after losing the first set and tore his shirt during the match, was left fuming after umpire Carlos Bernardes gave him a time violation when changing his shirt.
"He was the star of the show. That's what he wanted to be today," the 29-year-old told reporters.
"But there are definitely things that I need to regain from the emotional, mental point of view."
Bautista Agut said aggressive tactics were key to him picking up his first victory in six attempts against Djokovic.
"I tried to force him to play his best tennis. I think in the first set he played some good tennis. He played a little bit better than me," Bautista Agut said.
"But then I knew that I had to increase my level. I had to play more aggressive."
World number two Murray took a strong hold of his match against Simon after breaking the Frenchman's serve to clinch a tight first set.
Murray, bidding for his third Shanghai Masters title, carried his momentum into the second set as he broke Simon's serve twice to wrap up the match in one hour 43 minutes.
Bautista Agut, who has lost to Murray in their two previous meetings, will face the 29-year-old Scot in the final on Sunday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
