Barefield was a perfect 6-for-6 in the first half and finished the game 8 of 12 from the field. He got plenty of help from David Collette (17 points, eight rebounds) and Tyler Rawson, who recorded a double-double with 16 points and 10 rebounds.
Gary Blackston led four Panthers in double figures with 18 points. Dennis Jones added 13 points and Shaquille Preston and Zachary Hamilton each scored 11 points.
The Utes (1-0) led wire-to-wire with Barefield being fouled on a 3-point attempt in the game's opening moments. Barefield connected on all three free throws and the Utes were off and running.
While Utah never was threatened, the Panthers (0-1) were able to hang around and never trailed by more than nine points in the first half.
An old-fashioned three-point play by Adrian Hamilton at the 1:44 mark made the score 34-31.
And that's when Barefield took over.
A two-point finger-roll layup and a long-range 3-pointer to close out the half gave Barefield 16 points in the opening 20 minutes and put the Utes up 39-31 at intermission.
The Utes opened up the second half on a 19-0 to kill any idea that Prairie View had of making a comeback. Blackston ended the Panthers' drought with a layup at the 13:11 mark.
Kolbe Caldwell's floating jumper put the Utes up 62-36 for their largest lead of the game midway through the second half.
Utah was without the services of center Jayce Johnson who sat out as he recovers from an ankle injury.