Moniz completed 20 of 33 passes for 178 yards and a touchdown, but he did most of his damage on the ground running 14 times for 121 yards and three scores.
Moniz broke loose in the second quarter on scoring runs of 56 and 14 yards to give his team a 17-0 halftime lead.
Hansen finished the game with 16 completions in 30 attempts but he often seemed to be under pressure and throwing off balance under a fierce pass rush that was aided by the loss of sophomore left tackle David Bakhtiari to an injury early in the game.
Freshman place-kicker Will Oliver added the first field goal of his career, but the Buffs too often put themselves in bad spots with penalties and an offensive line that allowed Hansen to be sacked seven times.
The Buffs racked up more than 250 yards rushing against Hawaii in a victory in Boulder in 2010, but the running game was not effective in the first outing of 2011.
Senior running back Rodney Stewart's quest to become the program's all-time leading rusher began with just 52 yards on 18 carries. Stewart did have four receptions for 98 yards, mostly on screen passes.
Colorado cut the lead to 24-17 early in the fourth quarter but didn't manage to score again. Hawaii added 10 more points on Moniz's only touchdown pass to Joey Iosefa and a 22-yard field goal from Tyler Hadden.