Tai Wesley also scored 14, while Wilkinson pulled down a team-high 10 rebounds for the Aggies (16-6, 6-1 Western Athletic Conference).
After trailing by double digits most of the first half, the Wolfpack brought the score to 49-41 with 16:45 to play on a Kemp free throw.
But the Aggies answered behind inside play from Wilkinson and two 3-point shots from reserve guard Tyler Newbold and stretched the lead to 17 points, 71-54, with four minutes to play.
The Wolfpack only shot 1-of-8 on 3-point attempts in the second half, 6-of-18 for the game.
In the first half, USU burst out to a 13-2 lead, behind an 11-0 run and eight points from Wilkinson. Carroll dropped in 17 points and shot 6-for-11 from the field in the half, as the Aggies held a 47-36 edge at halftime.
USU shot 68 percent from the field in the first half, while Nevada shot 43 percent, 39 percent for the game.
The WAC rivals meet again in nine days in Reno, Nev.