The Friars held a two-point lead with 9:48 to play, but Baylor outscored Providence the rest of the way 23-10.
Baylor's semifinal opponent next Tuesday in New York will be Brigham Young, which eliminated Southern Mississippi earlier in the evening. The other semifinal will send Maryland against Iowa.
Jefferson hit 10-of-14 from the field and scored 26 points. Jackson was good on all seven of his free throw attempts and delivered 20 points.
Baylor hit 52 percent from the field and turned the ball over only five times.
Three Providence players accounted for all but four of their team's points. Bryce Cotton scored 23, Vincent Council had 21 and Kadeem Batts had 20.