Peterson had a 41-yard TD run late in the fourth period and Clint Ingram scored on a 50-yard interception return for the Sooners (1-1), who were upset last week by Texas Christian.
Paul Smith threw for 246 yards and a touchdown while completing 24-of-36 passes for the Golden Hurricane (0-2). Tulsa's Garrett Mills caught 13 passes for 152 yards.
After Peterson's one-yard touchdown run gave the Sooners a 7-0 lead, Brad DeVault kicked three straight field goals to give Tulsa a two-point lead late in the third quarter.
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