Putney finished with 22 points, 10 rebounds and five steals, while Williams added seven assists, six rebounds and a game-high 11 free throws.
UMass (16-5, 5-2) held a 23-21 lead before Williams hit a jumper, sparking an 18-5 run and helping the Minutemen take a 41-26 lead with 2:20 left in the first half. Putney scored 10 points during the run, including two 3-pointers, and Williams added six.
The Minutemen pushed their lead to 19 in the second half and did not allow the Billikens (16-5, 4-3) to get any closer than five.
Brian Conklin led Saint Louis with 17 points but the Billikens shot just 34.3 percent (23 of 67) from the field compared to 50 percent (25 of 50) for UMass.