Quincy Acy, the only senior in Baylor's starting lineup, had a double-double to lift the Bears past Xavier 75-70 and into its second regional final in three years.
Baylor will face the Kentucky-Indiana winner in Sunday's South Regional final.
Acy had 20 points and 15 rebounds. He sank two free throws with 31 seconds remaining after Xavier cut the Bears' lead to six points.
Baylor, wearing neon-green uniforms, never trailed and led by 18 points less than 8 minutes into the game.
But Xavier never quit, and cut the lead to just three, 71-68, with 22 seconds remaining.
Quincy Jackson had 16 and Perry Jones III had 14 for the Bears, the No. 3 seed.
Tu Holloway led Xavier, the No. 10 seed, with 22 points.