Iowa State (2-0), which struggled against Portland State's zone in the first half, held a two-point halftime lead and opened the second half with a 10-1 run for a 43-32 lead.
The Cyclones extended their lead to 14 points before Portland State rallied back.
Schroeder hit a pair of 3-pointers during a 14-4 run that brought the Vikings within four points with about 9 minutes left.
The Vikings remained close until the final 2 minutes, but the Cyclones put the game away by making eight of nine free-throw attempts in the last 50 seconds.
Iowa State plays Howard at 8 p.m. Friday in the second round of the tournament.
Portland State and Iona play at 5:30 p.m. Friday.
Story provided by Fox Sports