Alan Williams, Jaime Serna and Kyle Boswell had nine points each for the Gauchos (16-9, 10-4 Big West), who moved into a second-place tie with Cal State Fullerton in the conference standings. The teams split two games this season.
Nunnally and Boswell scored seven points each during a 16-1 run over a 4:30 stretch of the first half. Nunnally's 3-pointer gave UC Santa Barbara a 32-16 lead, and it maintained a comfortable cushion for almost the rest of the way.
Cal Poly got within 49-42 in the second half, but Nate Garth made a 3-pointer, and Johnson followed with a 3 and dunk as the Gauchos quickly regained control.
Authorities say former Michigan State basketball player Keith Appling has been charged with carrying a concealed weapon and other crimes.
Point guard Jaylen Fisher, who reopened his recruitment after coaching changes at UNLV, has committed to TCU over a long list of schools.
Forward Kennedy Meeks, who has averaged 9.4 points and 6.5 rebounds at North Carolina, has pulled out of the NBA draft and will return to the Tar Heels.