Joseph Chartouny's jumper with 2:37 left capped Fordham's scoring and made it 67-62. George Mason scored a pair of baskets in the final two minutes but missed two attempts to go ahead in the final 14 seconds.
Raut hit back-to-back 3-pointers to give the Rams (8-15, 3-8 Atlantic 10) their first lead in over 27 minutes at 58-56 with six minutes to go.
The Patriots (10-14, 4-7) tied it at 58 and retook the lead at 61-60 with 4:22 left. Fordham took the lead for good on the next possession with Cavit Havsa's layup.
George Mason scored 21 straight in the first half to lead 25-8 and led again by 17 at 33-16 late in the first period. Fordham made 10 3s in the second half to help close the gap.
Will Tavares had 11 points and 11 rebounds and Chartouny added 11 points for the Rams.
The rebuilding Wildcats are set to raise the 2018 national championship banner next week -- and also lower expectations for the season to come after multiple NBA departures.
Former Memphis All-American and NBA All-Star Penny Hardaway tipped off his first camp as new coach of the Tigers, and he's "really anxious" to get to work.