Arias threw for 319 yards and two touchdowns and Finney rushed for 88 yards and two touchdowns. Arias now has 55 touchdown passes for his career, tying Jason Whitmer for most as a Bengal.
Madison Mangum caught eight passes for 130 yards.
Idaho State (6-3, 4-1 Big Sky Conference) has won four straight games for the first time since the 2002 season.
The Bengals jumped out to a 14-0 lead when Arias hit KW Williams on a 6-yard scoring strike and Finney scored from the 5. Portland State (3-6, 2-3) answered in the second when Kasey Closs pulled in a 16-yard scoring pass from Kieran McDonagh. Both teams added a field goal to make it 17-10 at the half. The Bengals added two more touchdowns in the second half to seal the win.