Matt Carlino made three 3-pointers in the final minute and 30 seconds, and the Cougars made a late rally to cut an 11-point deficit to three with under 45 seconds to play, but the Bears made enough free throws to keep a comfortable cushion.
Carlino's 3-pointer with 7:39 tied the score at 52-52, but the game changed about 15 seconds later when Baylor's Cory Jefferson slammed in a dunk, and was fouled by Brandon Davies, his fourth.
Tyler Haws missed a tough 12-footer, then was called for an offensive foul along the sideline after a Baylor miss, and Jefferson hit another jumper to give the Bears a 57-52 lead.
Haws made a couple of free throws to get BYU within three, but Jackson then went to work, and the Cougars were finished. He had 24 points.
Haws led BYU with 25 points and Carlino had 19. Nate Austin had 11 rebounds and nine points, all in the first half.
Baylor took a 35-33 lead into halftime after Taurean Prince tipped in a missed shot with a few seconds left in the first half.
The Cougars started well, with Davies picking up two quick baskets, including a putback dunk. Austin hit a pair of jumpers in the first 10 minutes, and the Cougars had a 17-13 lead at the second media timeout.
However, Davies went to the bench with his second foul with eight minutes left in the first half, and Baylor took its first lead, 24-21, since its was ahead 2-0.
Carlino briefly left the floor in the first half with what BYU officials said was an issue with his right leg, but returned.
Carlino's jumper with 1:10 left in the half tied the score at 33-33, but Prince followed a miss with a tip-in to give the Bears (21-14) the slim halftime lead.