Louisiana Tech's Zac Champion threw for 144 yards on 16 of 27 passing, and the Bulldogs lost their fourth straight.
Danny Horwedel missed a 42-yard attempt in the third quarter and Ole Miss' Brandon Jenkins blocked a 36-yard field goal attempt late in the fourth quarter. Dustin Mouzon returned it 55 yards for the final score.
The two teams combined for four turnovers in the first half, and it was one of those that helped give Ole Miss a 7-0 lead.
Defensive end Marcus Tillman fell on Louisiana Tech center Lon Roberts' errant snap in the shotgun formation on the second play of the game. Three plays later, Adams hit McCluster on a deep slant for a 28-yard touchdown 1:32 into the game.
It was the first touchdown since Sept. 30, 2006, for McCluster, who missed the first four games of the year with a shoulder injury and the last six games of last season with a neck injury.
After Joshua Shene put Ole Miss up 10-0 at the half with a 27-yard field goal in the second quarter, Adams hit Hodge for a 17-yard touchdown in the third quarter for a 17-0 lead.
Louisiana Tech committed 13 penalties for 117 yards and allowed Ole Miss' first shutout since a 31-0 win over Mississippi State on Nov. 27, 2003.