Tuttle has reached double-figure scoring in 24 consecutive games.
Junior guard Wes Washpun scored 16 for the Panthers (7-0), including four 3-pointers.
Northern Iowa used a 10-2 run to lead 14-4, but Richmond pulled to within four points, 14-10, after a 3 by Terry Allen. Washpun hit a 3 at 3:14 and the Panthers led 30-15 at halftime.
The Spiders opened the second half with a 13-6 run and pulled to within four, 50-46, on a layup by Davis with 57 seconds to play. Matt Bohannon hit five free throws in the final 25 seconds to keep the Spiders at bay.