A driving basket by Raivio with a little more than five minutes left in the game gave Portland a 51-39 lead, its biggest margin since an early 17-5 edge. But the Eagles battled back, closing to within 58-52 on a three-point play by Kevin Winford with 1:56 left.
Portland answered with a floater by Sikma to push the lead to 60-52 and closed it out by hitting four of six foul shots in the final 45 seconds.
Brandon Moore added 14 points for Eastern Washington, which hit just 1 of 9 from the floor and trailed 12-2 to start the game.
Former Michigan point guard Spike Albrecht will play for Purdue as a graduate transfer next season.
Only six major-conference teams have failed to win an NCAA tournament game since the turn of the century. When will each program snap the streak?
Bruce Weber's Kansas State team earned a share of the Big 12 title three years ago, but a lot has changed since then and the pressure is on.