The Bears got off to a spectacular start, taking a 14-2 lead in the opening 5:30, and then spent the rest of the game fighting off a team that had rallied from double-digit deficits in its previous two tournament games.
Xavier clawed back to within four midway through the second half, but fell behind by 12 before making another charge in the closing moments.
Tu Holloway's 3-pointer cut the Baylor lead to three with 21 seconds to go, but Heslip was perfect from the line down the stretch to send the third-seeded Bears into the South Region final against top-seeded Kentucky. It will be Baylor's second trip to a regional final in three years.
Heslip, whose nine 3-pointers carried Baylor to a third-round win over Colorado last weekend, hit two layups to spark the Bears' quick start against the Musketeers.
Baylor made 63 percent of its shots during the first 10 minutes and wound up hitting 50 percent from the field for the game. Quincy Acy was 8-of-11 and led Baylor with 20 points and 15 rebounds.
Pierre Jackson added 16 points for the Bears (29-7), Perry Jones had 14 and Heslip finished with 11.
Holloway had 20 points to lead Xavier (23-12), which came into the tournament as the region's No. 10 seed.