Providence held Cincinnati to two points over the final 2:28 after the Bearcats closed within one on a pair of foul shots from Cheikh Mbodj.
The Friars led by as many as 12 points in the second half and held on despite making only 2-of-17 from beyond the arc.
Kadeem Batts led the way for Providence with 24 points and Cotton added 11. The Friars climbed to 12-11 for the season and are 4-7 in the Big East Conference.
Cincinnati (18-5, 6-4) received 13 points from Sean Kirkpatrick and 12 from JaQuon Parker.