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.
Forward Kennedy Meeks, who has averaged 9.4 points and 6.5 rebounds at North Carolina, has pulled out of the NBA draft and will return to the Tar Heels.
Cal big man Ivan Rabb could have been selected in the top 10 of the NBA draft. Instead, he's returning to Berkeley to make himself, and the Golden Bears, stronger.
Devin Williams' decision last month to sign with an agent and enter the NBA draft has left West Virginia in a tough spot.