The host Rebels won their first under new Coach Billy Brewer as Kent Austin passed for 212 yards and freshman Bill Smith kicked two field goals.
Arkansas (2-1) threatened late in the game, moving to the Mississippi 23. But a penalty and a 12-yard sack of quarterback Brad Taylor ended the drive with a minute left.
Austin, who completed 19 of 34 passes, said the Rebels were "shaky at times but we stuck it out. When the time came, we did what it takes to win and that's what it comes down to."
In the second period, Buford McGee scored on a three-yard run and Smith kicked a 28-yard field goal to give the Rebels (1-3) a 10-0 lead. Smith's 37-yard field goal in the third period made it 13-0.
The Razorbacks, capitalizing on Taylor's passes of 29 yards to Mark Mistler and 26 yards to Keith Kidd, scored on Taylor's two-yard keeper late in the third quarter.
They drove to the five in the fourth quarter, but settled for Greg Horne's 27-yard field goal after an illegal motion penalty negated Taylor's pass to Mistler in the end zone.