PRINCETON, N.J. — Stony Brook may be a top 10 team in men’s lacrosse, but the Seawolves are no lock for an NCAA Tournament bid if they don’t win the America East Tournament next month. And to build a resume strong enough to have a shot at an at-large bid, they couldn’t afford a slip on the slick turf Saturday against a struggling Princeton team enduring a turbulent week.

Fortunately for the visiting Seawolves, a crucial penalty against Princeton early in the fourth quarter gave them a key extra-man opportunity. Senior midfielder Challen Rogers took advantage, scoring his fourth goal of the game to help No. 8 Stony Brook hold off upset-minded Princeton and come away with a 13-10 victory at Class of 1952 Stadium.

Princeton’s Zach Currier, whose second goal of the game brought the Tigers within 11-10 with 11:12 remaining in the game, forced a turnover and was starting off on a fast break when Princeton was flagged for having too many men on the field.

“That was a big break for us,’’ Stony Brook coach Jim Nagle said of the penalty call. “They were scoring goals and they kept winning faceoffs. They do some really neat, kind of technical and confusing stuff on the ride and clear. And sometimes it bites ’em.’’

Princeton (2-7) was playing its first game under interim coach Matt Madalon, the offensive coordinator, who took over after former coach Chris Bates was fired Wednesday following an incident the previous Saturday in which Bates elbowed an opposing player during Princeton’s 19-8 loss to Brown.

Nagle expressed support for Bates, who had a 53-42 record in seven seasons at Princeton after succeeding coach Bill Tierney. “It was a tough week for their program, and Chris Bates is a class act,’’ Nagle said. “And one knee-jerk reaction doesn’t define him as a coach or a person.’’

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With the temperature at a chilly 43 degrees at the opening faceoff and the game played in a constant rain with the stadium lights on, Princeton scored the first goal of the game. But Stony Brook (9-2) shook that off and seemed to be in total control when Rogers scored his third goal to put the Seawolves up 7-2 with 7:42 left in the first half.

Princeton — which dominated faceoffs and ground balls — scored four straight goals to pull within 7-6 early in the third period. Stony Brook responded with a 4-1 run to go up 11-7, but Princeton scored three straight to put a scare in the Seawolves.

“It’s a game of runs,’’ Rogers said. “Obviously, every time we get a man up, we want to score. Our man up’s pretty good. We want to capitalize, and during that situation, we wanted to go out and bury one.’’

Notes & quotes: Princeton faceoff man Sam Bonafede, a sophomore from Bay Shore and Chaminade, had a career day, winning 19 of 27 and scoring his second goal of the season . . . Princeton got 35 ground balls to Stony Brook’s 16 . . . Stony Brook returns to action at 7 p.m. Tuesday at home with a non-conference game against Marist.