Galloway accounted for five of Saint Joseph's 10 3-pointers, Jones hit three more from deep and Kanacevic was a perfect 5 of 5 from the free-throw line.
C.J. Aiken pulled down 10 boards for Saint Joseph's (11-7, 2-3).
Semaj Christon had 16 points for Xavier (11-8, 4-2) but made just 8 of 21 shots. The Musketeers shot 21 of 61 as a team and made just 1 of 13 3-point attempts.
Saint Joseph's scored 15 points off 12 turnovers, compared to four points off 12 for Xavier.
Xavier trailed 30-26 at halftime but rallied to a 45-41 lead on a jumper from Christon. Travis Taylor's dunk made it 47-43 Xavier but the Musketeers were held scoreless over the final 5 minutes.