Iowa (2-1) was tenacious on defense, holding the Bears to just 36 percent shooting from the floor while forcing 23 turnovers.
The Hawkeyes shot 50 percent in the opening half, but Northern Colorado (1-2) trailed by just six at the break, using a stifling defense to force Iowa into 14 first-half turnovers.
The Bears used a 10-3 run to begin the second half to take a 30-29 lead as Iowa went 7:44 without a basket. But Peterson took charge, scoring a lay-up at the other end and drawing the foul. He missed the foul shot, but Seth Gorney snared the rebound and Peterson scored on another lay-up.
Iowa extended the lead to 38-32 with 9:00 remaining on a Gorney jumper, but a pair of 3s from Thanasi Panagiotakopoulos tied the game.
Iowa later went on a 9-2 run, capped by two Kurt Looby free throws to push the lead to 49-42.
Justin Johnson -- who entered play averaging 21 points a game -- was scoreless until he hit a 3 with 4:40 left in the game to push Iowa's lead to five.
The Hawkeyes hit on 8-of-10 free throws down the stretch and they didn't look back.
Sean Taibi led the Bears with 11 points.