Skinner, who has 386 Division I wins, is in his first season as head coach since the 2009-10 season at Boston College.
The Owls (1-4) grabbed a double-digit lead at 56-44 on Nigel Pruitt's 3-pointer with 6:53 left and held it until Mason Archie's 3 for IUPUI (2-3) cut the deficit to nine with 1:48 left.
Archie's layup with 37 seconds to go made it 68-62, but the Jaguars would get no closer.
Pruitt added 13 points, Nick Masterson scored 12 and Kendrick Ray 10 for Kennesaw State. The Owls led 30-28 at the break and pushed to a 41-34 lead early in the second.
Archie had 12 points and Jordan Pickett scored 11 for IUPUI. Nick Osborne and T.J. Henderson scored 10 each.