Rice was seeded sixth in the west division, Marshall third in the east. The Owls advance to a Thursday quarterfinal against UAB, second seed in the west.
Max Fiedler had 15 points and nine rebounds for Rice (15-12). Cameron Sheffield added 10 points.
Jarrod West had 19 points, seven assists and six rebounds for the Thundering Herd (15-7). Mikel Beyers added 17 points and eight rebounds. Taevion Kinsey and Jannson Williams each scored 11 points.
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