After an early 13-12 deficit, the Cardinal used a 19-4 spurt to build a 35-24 halftime advantage.
Santa Barbara came within 35-30 2:45 into the second half, but got no closer.
Stanford's Robin Lopez had 12 points and three rebounds. Landry Fields and Drew Shiller scored six points apiece, and Mitch Johnson added seven points and five assists, as the Cardinal rose to 6-3 in the all-time series between the two teams.
Santa Barbara's Alex Harris scored a team-high 18 points. Chris Devine had 14 points and eight rebounds, but no other player scored in double figures for the Gauchos (2-1) -- who were done in by 34.5 percent shooting (20-of-58) from the floor.