Providence overcame a seven-point deficit early in the second period to set up a second-round meeting with Robert Morris, which shocked 2012 NCAA champion Kentucky 59-57 Tuesday.
Cotton scored 25 points, hitting four 3-pointers and going 7-of-8 from the foul line. Vincent Council added 16 points for Providence (19-14), which failed to reach the quarterfinals of the Big East Tournament after losing to Cincinnati.
Charlotte (21-13) dropped a quarterfinal encounter to eventual champion St. Louis in the Atlantic 10 Tournament.
The 49ers were led by Victor Nickerson with 14 points.