Dimitri Batten added 13 points for the sixth-seeded Monarchs (16-16), who will face third-seeded Middle Tennessee in the quarterfinals on Thursday.
Kareem Canty scored 17 points and Shawn Smith added 15 points and 11 rebounds for the 14th-seeded Thundering Herd (11-22), who beat Florida Atlantic in the first round on Tuesday.
Old Dominion, playing its first game of the tournament, opened the second half with an 8-0 run after leading 24-22 at the break and Marshall never got closer than three after that.
The Monarchs have won two in a row for the first time since a four-game run from Jan. 4-18.
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