Led by Chris Duarte's 23 points and a team shooting 11-for-25 from three-point range, Dana Altman's squad will now face the winner of the USC (6) vs. Kansas (3) game in the bracket's West region.
Oregon shot 38-for-68 (55.9%) from the field.
Luka Garza led Iowa with 36 points, and Joe Wieskamp added 17. Patrick McCaffery was the only other Hawkeye in double-figures with 10 points.
Iowa finishes the year with a 22-9 record.
"You know, we did a lot of really, really good things this year, and it just hurts that we weren't able to, you know, be able to do it when it mattered most," Garza said postgame.
Head coach Fran McCaffery said he was "truly blessed" to have coached Luka, and that the school "may never see another like him."