Mississippi State (2-2) scored first and led at half, but could never put the visiting Bulldogs away.
Late in the fourth quarter with the game tied 20-20, Louisiana Tech (1-3) went on a nine-play, 60-yard drive and had the ball in field goal range with less than four minutes to play. But an interception by Jonathan Banks ended the drive.
Neither team was able to generate any offense in the final minutes.
In overtime, Mississippi State won the toss and elected to play defense. Whitley, a free safety from Jackson, Miss., intercepted Isham on the second play from scrimmage. Two plays later, Relf hit Perkins for his first completion since the third quarter, ending a streak of seven straight incomplete passes to end regulation.
Perkins finished the game with 47 yards rushing and had two catches for 22 yards, including the game winner.
Relf was 14 of 29 for 165 yards guiding the struggling MSU offense.
Isham, a 17 year-old freshman, finished 29-of-40 for 228 yards, but he was sacked three times and picked off twice.
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South Carolina's loss to The Citadel, coupled with Georgia and Florida struggling in tight victories, was an embarrassment for the conference.
The Utes and Buffaloes will try to overcome injuries to key contributors Britain Covey (Utah) and Sefo Liufau (Colorado) on Saturday.
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ESPN Big Ten reporter Dan Murphy breaks down the news that Michigan State QB Connor Cook will be a game-time decision for the Spartans game against Penn State.
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