The Bears, who won their first 17 games this season, found themselves trailing by 10 in the early going against a team making its first NCAA appearance.
Baylor then came back to lead by eight at the break and held on to set up a third-round meeting with Colorado, which surprised Nevada-Las Vegas in the last of the 16 tournament games played Thursday.
Seeded third in the South region, the Bears claimed 12 offensive rebounds to just four for the Jackrabbits.
Jackson scored 18 points and Brady Heslip had 17 for Baylor (28-7). Perry Jones III claimed 11 rebounds for the Bears, who fell in the Big 12 Tournament title game to Missouri after surprising Kansas in the semifinals.
South Dakota State, regular-season and tournament champion of the Summit Conference, was paced by 19 points from Nate Wolters. The Jackrabbits ended their season at 27-8.
Celebrity Families of 2014 [PHOTOS]