Grooms’ 5-yard TD run in double-OT came after the Thundering Herd (2-2) held the Owls (1-3) to a field goal on their possession.
Groom had 103 yards rushing on 12 carries, Steward Butler added 166 yards and a TD on 18 carries, and Marshall finished with 334 yards on the ground. Rakeem Cato was 28 of 39 for 259 yards and two touchdowns.
That was enough to overcome Rice quarterback Taylor McHargue, who threw for 314 yards and three TDs while also rushing for 153 yards and a score.
McHargue scored on a 43-yard run with 3:17 left in regulation, and Rice added a 23-yard field goal by Chris Boswell with no time left to send the game into overtime.