The Atlantic Coast Conference player of the year had made just 20 of 60 shots (33 percent) and 7 of 31 3-pointers (23 percent) in his last four games. But he had 19 points by halftime in this one, helping the Tar Heels (28-7) quickly eliminate any chance of an unprecedented upset.
Jackson, a 6-foot-8 junior, finished 8 of 13 from the field and 5 of 8 from 3-point range with seven rebounds.
Isaiah Hicks added 17 points and Kennedy Meeks had 13 for the Tar Heels, who are a No. 1 regional seed for an NCAA-record 16th time.
Kevin Scott scored 19 points to lead the 16th-seeded Tigers (23-12), the champions of the Southwestern Athletic Conference.
SWAC player of the year Zach Lofton struggled, finishing with nine points on 2-for-11 shooting.
The Tar Heels lost the chance to open in their home state when the NCAA yanked games from Greensboro due to that state's passage of a law limiting protections for LGBT people.
The games moved to South Carolina - the state's first chance to host since 2002 - after it removed the Confederate flag from state capitol grounds in 2015.
Texas Southern: The season marked another sign of solid footing for the Tigers under former Indiana coach Mike Davis in the SWAC. This marked three NCAA appearances in four seasons going back to 2014 and 2015.
UNC: Jackson's recent shooting funk was the most obvious concern as it started its push to return to the Final Four after losing in last year's title game. The Tar Heels entered Greenville on a down note after losing to rival Duke in the ACC Tournament semifinals.
The Associated Press contributed to this report.