Peak finished with 18 points for the Hoyas (7-3), who opened strongly in both halves. They led by 14 in the first before Charlotte (6-5) closed on a 7-0 run to get within 38-31.
Georgetown built its lead back to 60-44, but the 49ers used another 7-0 run to get to 70-63 and Braxton Ogbueze's back-to-back 3s pulled Charlotte within 77-75 with 3:13 to go.
Keyshawn Woods' basket with 8.6 seconds left pulled Charlotte within 79-78. But Peak's free throws put the Hoyas back up by three and Woods missed a well-defended 3-point attempt in the final second.
Jabril Trawick added 11 points and 10 rebounds for Georgetown.
Woods led Charlotte with 16 points.