Smith now has 1,018 yards rushing this season and he also became the 10th player in FBS history to top 4,000 rushing yards and 1,000 receiving yards in a career.
The win makes the Golden Eagles (6-4, 4-2 Conference USA) bowl eligible for a third straight season.
But Rice (1-9, 1-5) continually fought back behind Nashon Ellerbe, who had 153 yards and four touchdowns on 22 carries.
Twice Ellerbe had the Owls within two points on TD runs of 17 and 1 yards, but Southern Miss answered with Griggs' 47-yard TD strike to Robertson and Smith's 18-yard TD run with 2:55 to play preserving the win.
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