Mike McCall Jr. had 10 points and seven rebounds for the Billikens (23-6, 11-4 Atlantic 10), who moved a half-game behind first-place Temple in the league standings. The Owls, however, hold the tiebreaker, a 72-67 victory against St. Louis in January.
The Billikens clinched a top-four seed and bye in next week's Atlantic 10 tournament.
Xavier led 39-29 at halftime but shot just 28 percent (7 for 25) afterward. That helped St. Louis take control with a 24-2 run over an 8:34 second-half stretch.
Conklin had 11 points and McCall hit two 3-pointers during the surge, which gave the Billikens a 53-42 lead with 9:44 remaining. The Musketeers got no closer than seven points the rest of the way.