Anthony missed the front end of a 1-and-1 and the Spiders led 55-53 with 20 seconds left. IUPUI's Mason Archie II missed a jumper with 5 seconds left and Richmond's Trey Davis sealed it with two free throws.
Anthony made 6 of 10 shots to move into 10th place on Richmond's career scoring list.
ShawnDre' Jones added 11 points for Richmond (7-4).
Alonzo Nelson-Ododa hit his first basket of the game, a 3-pointer, with 2:46 left to give Richmond a 51-47 lead.
Archie led IUPUI (3-9) with 12 points and Elijah Ray added 11.
IUPUI started the second half on a 14-3 run to take a 36-32 lead. Anthony stopped the run with his second 3-pointer of the half to end Richmond's 6-minute scoring drought.