Shaquille Johnson made a layup with two seconds remaining to give Marshall a 63-61 victory against Rice on Saturday night.
Damier Pitts scored 18 points for the Thundering Herd (11-4, 2-0 Conference USA), and Johnson added 13. Dennis Tinnon had 10 points and 11 rebounds.
Tamir Jackson had the last shot for the Owls (9-7, 0-1), but his 3-point attempt with a second left missed. Omar Oraby had 16 points and 10 rebounds for Rice, and Arsalan Kazemi added 15 points.
Jackson, the Owls' leading scorer, was held to seven points on 3 of 15 shooting.
Johnson's 3-pointer gave the Herd a 63-61 lead with 3:55 remaining. Oraby tied the score with two free throws with 2:17 left.
Kazemi missed two free throws with 11 seconds to play.
The contest featured Marshall, the nation's No. 3 rebounding team at 42.6 a game, against the top individual rebounder in the country, Kazemi. The Herd won the boards battle 45-27 and limited Kazemi, who came in averaging 12.4 rebounds, to just four.