The win is the second in row over a ranked opponent for Offner and the Sachems (8-7-4), who defeated No. 13 Woburn, 3-2, Saturday.

“James is on the small side,’’ said Winchester coach Matt Stang. “He likes to come out and cut down on the angles and is a quick kid. He plays with a lot of poise for freshman and has been on a role as of late.’’

Senior winger Michael Marx netted the winner on the power play midway through the first period when he cleaned up the rebound on a shot from the point by Alex Sharp.

Midway through the third, Offner showed his poise, making his best save of the night, sliding to stop the Harbormen (13-4-1) on a 2-on-1 attempt.

The Sachems must win one of their three remaining games to earn a spot in the state tournament.

Boston Latin 5, Waltham 2 - Senior forward Kevin Cotrone had two goals and an assist for the Wolfpack (11-2-4).

Boys’ basketball

Dorchester 54, Latin Academy 46 - Facing a must-win situation in order to keep their playoff hopes alive, the visiting Bears held the Dragons to two field goals in the third quarter and erased a 9-point halftime deficit for the Boston City League win.

Dorchester (8-9), which faces off against O’Bryant tomorrow with a state tournament berth on the line, committed numerous turnovers and fell behind, 21-12, in the first half.

Jeduan Langston led Dorchester, scoring 12 second-half points to spark the rally.

Norwell 60, Hull 32 - Senior forward Nick Volpe scored 20 points, helping the Clippers give coach John Willis his 300th career win.

Somerville 61, Concord-Carlisle 57 - Senior guard Kevin Silva scored 23 points and Billy Bonnet and John Lubin combined for 16 points and 10 rebounds to lead the Highlanders.

Rockland 62, East Bridgewater 34 - Matt Nicholson (18 points), Tyler Gibson (16), and Devyn Flipp (13) led the Bulldogs (17-2).

Cohasset 60, Mashpee 45 - Shane Haggerty (24 points) and Kyrel Juandoo (16 points) led the Skippers (13-5), who held the Falcons without a field goal in the fourth quarter.

Carver 76, Harwich 66 - Senior captains Myles Dias (27 points) and Tevin Silva (16) led the Crusaders (15-4) past the Rough Riders.

Winthrop 57, Danvers 56 - The Vikings (14-5) clinched a share of the Northeastern Conference title behind Joe D’Amore’s game-high 17 points.

Girls’ basketball

Rivers 52, St. George’s 32 - Senior captain Tyra Melendez scored her 1,000th career point, leading the Red Wings (16-2).

Pentucket 49, Newburyport 30 - Coley Viselli’s 15 points helped the Sachems win their seventh in a row.