Four days after a 23-point loss at Coastal Carolina, Jennings and Harrison scored 15 points each as the Tigers (7-4) beat South Carolina State for the 11th time in 12 games.
Clemson, 28-1 against Mid-Eastern Athletic Conference teams, led by as many as 39 points in the second half.
Harrison, 6-foot-4 sophomore transfer from Brigham Young, hit 6 of 11 shots from the field and had four rebounds and six assists.
Jennings, a 6-9 senior, scored 15 points with four rebounds, two assists, a steal and a blocked shot.
Matthew Hezekiah scored 14 points off the bench to lead South Carolina State (4-9).
Point guard Rod Hall had six assists with no turnovers for Clemson, whose 22 assists on 30 field goals were a high under coach Brad Brownell.
Fueled by Adonis Filer's eight points off the bench, Clemson finished the first half with a 21-2 run for a 36-18 lead.
South Carolina State led 16-15 after a 3-pointer by Luka Radovic with 9:03 to play but went scoreless for the next 5 minutes, 34 seconds.
Harrison hit a 3-pointer for an 18-16 Clemson lead with 8:38 to play and the Tigers never trailed again.
The Bulldogs' only score over the final nine minutes of the half was a dunk by Hezekiah with 3:39 to play.
South Carolina State committed 18 turnovers to Clemson's nine and shot 31 percent (18 of 58) from the field to the Tigers' 49.2 percent (30 of 61).