The Sooners will face Santa Clara in the semifinals Friday. Washington State will play New Mexico in the consolation round.
Newell shot 7 of 13 and hit four 3-pointers, and Steven Pledger added 14 points on three 3s.
The Sooners were stout defensively, forcing 22 turnovers and limiting the Cougars to 22 percent shooting in the second half.
Brock Motum led Washington State (2-2) with 13 points. Faisal Aden had 12.
Oklahoma trailed by a point when Newell took over. He accounted for all but three points of a 13-2 run, capping it with a 3-pointer for a 60-50 advantage with 7:15 remaining.
Marcus Capers heaved in a 60-foot shot that beat the halftime buzzer and gave Washington State a 40-38 lead.
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