Ryan Butler and Dan Geriot each had 15 points for the Spiders (8-7, 1-1), who had their four-game winning streak stopped.
Trailing 11-4 six minutes into the game, the Hawks went on a 25-3 run, highlighted by three 3-pointers by Calathes, to take a 29-14 lead.
Richmond responded with a 15-7 run, including seven points by David Gonzalvez, and closed within 36-29 at the half.
Saint Joseph's started the second half with another outburst, scoring 22 of the next 25 points. Calathes scored 11 in the run and the Hawks led 58-32 with 11:11 left.
The Hawks have averaged 80 points during their streak and now hold an 11-2 edge over Richmond in the all-time series.
