Nevada (3-2, 1-0 Western Athletic Conference) racked up 507 yards of total offense against the Vandals.
Kaepernick went 19-of-24 for 243 yards with no interceptions, and Taua had 94 yards on 21 carries.
Idaho (1-5, 0-2) had a chance to go up first when kicker Tino Amancio attempted a 39-yard field goal midway through the first quarter, but it was blocked by Nevada's Chris Stack.
Nevada took over on its own 22 and drove to Taua's 3-yard touchdown run.
The Wolf Pack made it 13-0 when Idaho punter T.J. Conley muffed a punt from the Idaho 1-yard line. Conley had the ball, but as he moved his arms into punting position he dropped it and Nevada's John Bender fell on it. Taua then ran in from the 1.
Enderle later connected with Williams for a 12-yard touchdown, but by that time the Wolf Pack had racked up 42 points.
Enderle led the Vandals with 226 yards, going 18-of-36 with two touchdowns and no interceptions. Williams had 10 catches for 142 yards and two touchdowns.
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.