Ferrer seemed on track for another title when he took the first set. But the 26th-ranked Sock broke the eighth-ranked Ferrer's serve in the second game of the second set and held for 3-0, and was never threatened the rest of the way.
Sock advanced to his third ATP Tour final after finishing runner-up indoors at Stockholm last year and winning on clay in Houston.
"I knew coming in I had to play some unbelievable tennis and fortunately I was able to do that," Sock said. "It was a difficult day, started out I woke up with some flu-like symptoms and didn't know if I was going to be able to play.
"I ended up coming out and playing some of the best tennis of my career so maybe I can stay sick to Melbourne if I play like this."
The 10th-ranked Tsonga seemed in control of the second semifinal but Bautista Agut, ranked No. 25 and bidding for his third career title, slowly turned the match in his favor and he converted one service break in the third set to confirm the win.
No. 3-seeded Victor Troicki and No. 4 Grigor Dimitrov will meet in the final at the Sydney International after a day featuring quarterfinals and semifinals, with organizers catching up following rain delays.
Troicki beat Nicolas Mahut 4-6, 6-3, 6-3 in the quarterfinals and then had a 3-6, 6-4, 6-4 win over Teymuraz Gabashvili, who reached the semifinals when Bernard Tomic retired from their quarterfinal match because of possible food poisoning.
"I was just feeling a little bit sick last night and was very difficult to play two matches today," Tomic said.
In the women's semifinals at Sydney, two-time Grand Slam champion Svetlana Kuznetsova beat top-seeded Simona Halep 7-6 (5), 4-6, 6-3. Kuznetsova's final opponent will be Monica Puig, who advanced when Belinda Bencic retired ill after losing the first set 6-0.
At the Hobart International, Eugenie Bouchard, playing her best stretch of tennis since sustaining a concussion in a dressing room fall at the U.S. Open last September, advanced to the final with a 6-1, 4-6, 6-4 win over third-seeded Dominika Cibulkova of Slovakia.
"I can't remember the last time I played that well," Bouchard said. "The important thing is trying to keep that and have that consistently."
That consistency wasn't there in the second set, when she lost every service game. She smashed her racket while walking off the court at the end of the set and said her play was "absolutely disgusting."