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.
TCU had a lot to overcome, from torrential rains to an ankle injury that slowed Trevone Boykin, but the Horned Frogs dug deep to knock off Baylor.
Check out highlights from TCU's 28-21 double-overtime win over Baylor.
In a game that was marked by inclement weather, TCU prevails for the victory over Baylor in double overtime.
SEC Nation previews the Ole Miss vs. Mississippi State matchup.
SEC Nation previews the matchup between in-state rivals Florida and Florida State.
Players and coaches from Alabama and Auburn discuss the tradition of the Iron Bowl and the 2015 matchup.