Gutierrez hit 5-of-7 field goals and was perfect in four free-throw tries.
He was one of four Cal players in double figures. Harper Kamp and David Kravish scored 12 for the Bears and Brandon Smith had 11 points.
Kamp and Richard Solomon led Cal (3-0) with nine rebounds apiece.
Josh Terry scored 16 points for Austin Peay (0-2). Melvin Baker scored 12 points and had a team-high six rebounds.
The Governors trailed 40-13 at halftime and their 42 second-half points were not enough to threaten Cal.