Mike McCall Jr. had 10 points and five assists for the Billikens (21-5, 9-3 Atlantic 10), who won their fifth straight and stayed a half-game behind first-place Temple in the conference standings. The Owls hold the tiebreaker.
Darien Brothers had 19 points for the Spiders (13-14, 4-8), who won the A-10 title and advanced to the NCAA tournament's round of 16 a year ago.
Richmond was within 44-41 with five minutes remaining. But Mitchell hit two 3-pointers and made two free throws to fuel a 13-2 run over a 2:41 stretch that enabled Saint Louis to pull away.
The Billikens had a 38-24 rebounding advantage, outscored the Spiders 30-24 in the paint and had an 11-3 edge in second-chance points.