Baylor, ranked No. 9 in the AP poll and seeded third in the South region, went on an 8-0 run midway through the second half after the Jackrabbits had gotten within three points, then held on after letting them get within four down the stretch.
Anthony Jones added 11 points and Quincy Miller had 10 for the Bears (28-7), who moved on to face either sixth-seeded UNLV or 11th-seeded Colorado, who were playing later Thursday.
Summit League champion South Dakota State (27-8) was led by Nate Wolters' game-high 19 points and 15 from Chad White. The 14th-seeded Jackrabbits made their first-ever appearance in the NCAA Tournament.
Baylor is a No. 3 seed for the second time in three years -- its highest ever placement in the NCAAs -- following a season that started 17-0 and included a loss to Missouri in the Big 12 title game on Saturday.
But it trailed by as many as 12 points in the first half and was squeezed by the Jackrabbits down the stretch.
Brayden Carlson's layup cut the Baylor lead to 47-44 inside 13 minutes. The Bears then used their 8-0 run to create some space, getting the final four points from Miller on a dunk and a layup.
Another Carlson layup and a three-pointer from Griffan Callahan sparked an 8-2 surge for South Dakota State, which pulled within 64-60 on White's three from the corner with 1:13 remaining.
The Jackrabbits never scored again while Heslip and Jackson sealed the Baylor win with two free throws apiece down the stretch. Among South Dakota State's misses near the end was a three-pointer from Carlson that was off with under 30 seconds remaining and the Jackrabbits trailing by four.
The Bears shot better than 44 percent from the floor, including 8-of-20 from three-point range. They had a 36-28 lead at halftime after overcoming deficits of 8-0 and 19-7.
South Dakota state went 10-for-30 on threes and shot 42 percent.
In 2010, Baylor was also a No. 3 seed in the South Region and advanced to the Elite Eight...The Jackrabbits beat Western Illinois in the Summit League championship last week to earn their bid...Baylor matched its record of 28 wins set in 2009-10 by the Elite Eight team that finished 28-8.