Ben Mockford chipped in with 9 points on 3-of-8 shooting from 3-point range for St. Francis (3-7).
Trailing 33-30 at halftime, Cannon's layup five minutes into the second half tied the game at 39.
The Terriers then went on a 24-11 run over the next 10 minutes to take a 63-50 lead with 5:07 left to play. Nichols finished off the run with back-to-back 3s. Colgate (3-9) failed to get within 10 the remainder of the game as St. Francis pulled away for the victory.
St. Francis made eight 3s in the final period and held Colgate to 37.9 percent (11 of 29) shooting in the second half.
Murphy Burnatowski led the Raiders with 19 points.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.