Warney was 10 of 18 from the floor with nine rebounds and five blocked shots. Lucas Woodhouse added nine points with five rebounds and five assists.
Stony Brook (6-4) used a 7-2 spurt, including a 3-pointer by Carson Puriefoy, to go up six with 3:43 to go. Brian Bernardi made a layup with 1:44 to cut the deficit to one, but Ahmad Walker responded with an inside basket, was fouled, and made the one-and-one for a four-point lead 1:23 left.
Hofstra was forced to foul, and Stony Brook made 3 of 4 from the line in the last 20 seconds to seal the win.
Ameen Tanksley scored 23 points to pace Hofstra (6-4). Bernardi finished with 22 points.