The Tigers (3-6) rallied from nine down deep in the second half to outscore Stony Brook 20-9 in the last six minutes.
Clay Wilson hit a 3-pointer to put Princeton ahead 57-55, and Cook converted a three-point play at 5:24 left for a 60-57 lead. Spencer Weisz, Wilson and Cook all hit 3-pointers in the final 4 minutes - Princeton hitting 12 of 26 from deep.
Stony Brook (5-4), despite a season-best 61-percent halftime shooting, trailed 38-36 at the break. Jameel Warney notched his nation-leading eighth double-double with 12 points and 13 boards for the Seawolves. Rayshaun McGrew added 18 points and 10 boards.