Williams led the Minutemen (3-2) with 23 points, and Terrell Vinson scored 18.
Evan Hymes led Siena (2-5) with 15 points, O.D. Anosike had 13 points and 13 rebounds, and Rob Poole scored 11.
Siena held a 63-60 advantage with 2:04 remaining but did not score again. Jesse Morgan’s layup with 51 seconds left pulled the Minutemen to 63-62.
Massachusetts took its first lead of the second half at 44-43 on Sampson Carter’s jumper with 11:54 left.
The Saints led 34-24 at the break, outshooting the Minutemen from the field 52.4 percent (11 of 21) to 31.3 percent (10 of 28). Massachusetts scored the last five points of the half on William’s 3-pointer and Vinson’s layup with 7 seconds left to close the gap.