Johnson ignited the decisive spurt with a tip-in midway through the second half that broke a 40-40 tie.
Wesley Gordon added a jumper and Johnson slammed through an offensive rebound to put the lead at six points. A free throw from Jaron Hopkins and two from Askia Booker had Colorado (12-2, 1-0 Pac-12) up 49-40 with 7:50 to go.
Oregon State (8-5, 0-1) got within five points late but Colorado put the game away with free throws.
Johnson ended up with nine points while Hopkins, Booker and Josh Scott tied for the Buffaloes' scoring lead with 13 points each. Scott also had 10 rebounds.
Roberto Nelson, fueled by 10-of-10 free-throw shooting, had 23 points for the Beavers but no other Oregon State player had more than eight points.
Swim Week Miami Beach 2014 [PHOTOS]