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.
New Hampshire beats Division III Mount Saint Vincent 100-61
Josh Hopkins scored 15 points, freshman Jayden Martinez had 14 points and eight rebounds and New Hampshire beat Division III Mount Saint Vincent 100-61 on Monday.
Ducks on upset alert this week
Will Villanova and Oregon survive tough tests this week?
Duke leapfrogs Kansas for No. 1 in latest AP Top 25 poll
Duke has supplanted Kansas atop the new AP Top 25 poll after its dominating win against Kentucky, giving the Blue Devils a record number of appearances at No. 1.