Xavier will meet Dayton in Friday night's semifinals after the Flyers downed St. Joseph's, 84-74.
In the evening quarterfinals, LaSalle shocked East Division champion Temple, 72-66, and Richmond got past St. Bonaventure, 78-69.
West, the league's regular-season MVP, did not take a shot in the first half and had only one rebound. Xavier (22-5) shot just 17 percent from the field during the opening 20 minutes, but made 12 of 15 free throws to hold its deficit to 28-21.
Romain Sato scored 21 points and Kevin Frey added 15 for Xavier. Shannon Crooks scored 16 points and Micah Brand added 15 and 12 boards for Massachusetts (13-15), which committed 21 turnovers and saw its postseason hopes come to an end.
West was plagued with first-half foul trouble and consistently drew a double team. But he rebounded to give Xavier the lead late in the game before Massachusetts sent it into overtime on an off-balance, three-pointer by reserve forward Eric Williams with seven-tenths of a second remaining.
Dayton overcame a 25-point effort by St. Joseph's Bill Phillips to advance to the semifinals as the No. 3 seed from the West Division.
Brooks Hall scored 13 points for the Flyers while Sean Finn and David Morris had 12 each.
Reggie Brown paced Richmond with 30 points as the Spiders look to get past upstart LaSalle and reach the league championship game.