Idaho (0-4) had tied the game on the final play of regulation, when Dominique Blackman tossed an 8-yard TD pass to Mike Scott in the corner of the end zone. Trey Farquahar's extra point made it 34-all.
Farquahar's 49-yard field goal put the Vandals ahead in overtime, but Smith and Claiborne pulled it out for the Cowboys (1-3).
Smith was 23 of 35 for 365 yards and was not intercepted, and Chris McNeill caught eight passes for 219 yards. Blackman finished 34 of 46 for 306 yards and had three touchdowns and no interceptions.
Florida State coach Jimbo Fisher hopes quarterback Sean Maguire is ready to go full speed by the middle of June.
Graduate transfer quarterback Davis Webb has officially joined California, giving the Golden Bears an experienced option to replace No. 1 overall NFL draft pick Jared Goff.
First-year football coach Dino Babers, hired by former Syracuse AD Mark Coyle, is on the committee that will search for Coyle's replacement.
Hugh Freeze has some major holes to fill on offense with the departures of Laremy Tunsil and Laquon Treadwell, but there is Chady Kelly and good depth.
After transferring in from Montana State, Dakota Prukop has a checklist he's working from as he prepares to compete for the Oregon job.
The destination for Week 6 of the Big 12 Ultimate Road Trip is unanimous, as all three conference reporters would head to the Red River Rivalry.