Tipsarevic, who won the decisive third point in Serbia's Davis Cup semifinal win over Canada on Sunday, squandered seven break points in the second set against Bautista Agut, who broke the Serb twice and closed the match with a backhand down the line on his first match point.
Earlier, sixth-seeded Ernests Gulbis of Latvia and seventh-seeded Lukas Rosol of the Czech Republic both advanced to the second round in straight sets.
Results from the third day of the ATP St Petersburg Open on Wednesday (x denotes seeding):
Guillermo Garcia-Lopez (ESP) bt Mikhail Youzhny (RUS x2) 6-4, 4-6, 6-3
Denis Istomin (UZB) bt Andrey Golubev (KAZ) 4-6, 6-3, 6-4
First round:
Michal Przysiezny (POL) bt Albert Ramos (ESP) 3-6, 6-4, 6-3
Lukas Rosol (CZE x7) bt Ricardas Berankis (LTU) 6-4, 7-6 (7/4)
Roberto Bautista (ESP) bt Janko Tipsarevic (SRB x3) 7-6 (7/4), 6-3
Ernests Gulbis (LAT x6) bt Michail Elgin (RUS) 6-0, 6-1
Sergiy Stakhovsky (UKR) bt Fernando Verdasco (ESP x5) 6-3, 6-4
Joao Sousa (POR) bt Paolo Lorenzi (ITA) 6-3, 6-4
Konstantin Kravchuk (RUS) bt Horacio Zeballos (ARG) 7-6 (7/5), 6-3