John made 1 of 2 free throws to cap an 8-0 run that gave the Wildcats the lead, 66-60, for good with 3:58 to play. Jon'te Dotson answered with a 3-pointer before the teams traded layups and Weber State led by three with 2:41 remaining.
Two free throws by Baker made it 70-65 25 seconds later, but Jordan Davis hit two foul shots before DJ Miles and Dotson each made 1 of 2 to pull Northern Colorado within one with 19 seconds left. Baker made a pair of free throws to make it 72-69 and, after an offensive foul, John hit two more to cap the scoring.
Davis led Northern Colorado (7-12, 3-5) with 21 points, but committed eight turnovers.
Weber State shot 50 percent from the field and scored 23 points off 21 Bears turnovers.
Jeff Capel Jr., the former Old Dominion and Fayetteville State coach, has died, less than two years after being diagnosed with ALS.
Vanderbilt scored a huge commitment on Monday when skilled scoring guard and immediate-impact player Darius Garland pledged to head coach Bryce Drew.
Duke's young standouts will have their first big test when the top-ranked Blue Devils meet No. 2 Michigan State in Tuesday night's Champions Classic.