Tartt was 2-for-2 from beyond the arc, while Harris hit 2 of 3 for the Great Danes (2-2) in the 2K Sports Classic. Albany outrebounded the Braves 43-26.
The Braves (0-4) stayed close early, and a Jonathan Boyd 3-pointer pulled Alcorn State to within 12-11 about 6 minutes into the game. But a pair of 3s from Harris and Mike Black fueled an 11-1 run and the Great Danes cruised from there.
Albany led by eight points at halftime and outscored the Braves 35-27 in the second half.
The Great Danes shot 46.4 percent from the field (26-for-56) compared to just a 35.1 percent mark (20-for-57) for Alcorn State.
Boyd led the Braves with 16 points and four steals.