Nesho Milosevic scored 15 points for the Highlanders (0-12).
Lucas converted a missed shot by Beauford just before the halftime buzzer to give the Seawolves (2-7) a 30-24 lead.
Stony Brook opened the second half with an 8-2 run capped by a breakaway layup by Eddie Castellanos with just over 17 minutes remaining.
Beauford's drive ended a 6-0 run that gave the Seawolves their largest lead of the game, 51-34, with just under 11 minutes to play.
New Jersey Tech used a 12-1 run to get within 55-51 on two free throws by Milosevic with 4:06 left. Lucas made two free throws for a 57-51 lead and Beauford scored Stony Brook's final five points, three on free throws.