The Great Danes (20-9), who have won four of their last six games, reached 20 wins for the first time since 2006-07 and for the third time in their Division I program history.
Trailing 16-15, Albany pulled ahead with a 7-0 run. The Great Danes then expanded their 27-24 halftime lead with another 7-0 burst to open the second half. Puk scored five points in the spree, and the Stags could get no closer than five the rest of the way.
Albany, of the America East Conference, recorded 11 steals, surpassing 10 steals for only the second time this season. The Great Danes outrebounded Fairfield 33-25.
Derek Needham's 15 points led the Stags (17-12), of the Metro Atlantic Athletic Conference, who came in on a two-game winning streak.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
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.