Stony Brook (19-5, 7-2 America East) sits alone in second place in the conference, trailing Vermont (8-1) by one game.
Jeff Otchere and Jaron Cornish added 11 points apiece for the Seawolves, who held the Bearcats to 36-percent shooting and outrebounded them 51-33. Cornish and Akwasi Yeboah each dished out six of Stony Brook's 21 assists.
Binghamton hit three straight 3s in a 9-2 run and closed to 41-34 in the second half, but the Seawolves replied with a 9-4 run and led by 16 with 12:21 to play and were never threatened.
Olaniyi, Yeboah, Latimer and Cornish each made 3s and the Seawolves jumped to a 22-10 lead, doubled the Bearcats at 37-18 and led 39-25 at halftime.
Morant: 'I still have a lot of more work to do'
Ja Morant talks with Marty Smith about his journey to Murray State and his rise to being recognized as one of the best players in college basketball.
Iowa's struggles could continue in tourney
ESPN bracketologist Joe Lunardi says No. 10 seed Iowa peaked too early and could be in for a big loss to No. 7 seed Cincinnati.
Don't sleep on Florida State as a Final Four contender
ESPN bracketologist Joe Lunardi won't be picking Florida State in his Final Four, but he says the Seminoles are capable of reaching Minneapolis.