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But they responded with two unanswered goals, controlling play for much of the remainder of the contest, to secure a 2-1 home victory over the 29th-seeded Shamrocks (10-6-4) at Memorial Park. “They showed character today,” said coach Jimmy Odierna. Needham (13-3-3) found the equalizer in the 26th minute, when senior midfielder Conor O’Brien cut in from the left wing and rolled a pass across the goal to junior forward Max Shoemaker. Shoemaker, alone at the back post, slotted the finish into the open net. “It calmed our nerves a bit, to say ‘Oh, okay. We got this now,’ ” Odierna said. Senior captain Avery Brodsky netted the winner in the 42nd minute. Following a series of one-touch passes that began near midfield, freshman midfielder Nils Svensson fired a shot at goal. His bid was saved, but Brodsky, a forward, got on the end of the rebound and slotted it home before racing to celebrate with the Needham student section. “We went down early, but we don’t have the heart to lose that game,” said Brodsky. Needham had plenty more chances to put the game to rest, taking 21 shots and putting 12 on frame. “We could’ve been easing our way through the end of that game if we had put the ball away a few more times,” Odierna said. The Rockets will host 13th-seeded Concord-Carlisle on Monday (6 p.m.) in a rematch of the 2023 state title game, which the Patriots won 2-0. “Next game we’re going to start off stronger,” said Brodsky. “We’re going to win the game earlier, and we’re going to get them by a lot of goals.” Division 1 State Winchester 2, New Bedford 1 — Junior Cole Queenan and senior Tom Duval each struck in the opening 20 minutes, which proved enough for the No. 28 Red & Black (10-3-4) to hold on for a first-round upset over No. 5 New Bedford (13-5). Division 2 State Northampton 4, Newburyport 2 — Senior Jasper Cantor and sophomore Justin Zaruma Buri netted a goal apiece in the first half and senior Charlie Ames added an insurance goal in the second half to propel the second-seeded Blue Devils (14-0-5) to a first-round triumph over No. 31 Newburyport (12-6-2). Division 4 State Cohasset 2, Maynard 1 — With less than a minute remaining in overtime, Brayden Dibona fired in the winner to lift the 17th-seeded Skippers (7-7-7) past No. 16 Maynard (9-5-5) in a first-round triumph on the road. Bryce Myers got on the board first for Cohasset, which hits the road again to face top-seeded Sutton (16-1-2) in the Round of 16. Uxbridge 4, Littleton 1 — After falling behind 1-0 in the first half, Gabe Gomes, Stephen Leach, Kameron Desroche, and Wilson OBiocha scored four answered goals for the No. 12 Spartans (12-3-4) en route to a first-round victory over No. 21 Littleton (8-8-3). Division 1 State Franklin 2, Waltham 0 — Senior Addi Weiss started the scoring in the second quarter and freshman Cade Taccini added an insurance goal in the fourth quarter to propel the No. 2 Panthers (15-2-3) to a second-round victory over No. 18 Waltham (12-5-3). Division 2 State King Philip 6, Dartmouth 2 — Abbey Pompei netted a hat trick, and goals from Stephanie LeBlanc, Brooke Santo, and Ella Morgan helped the fifth-seeded Warriors (16-4) take care of business in the second round against No. 12 Dartmouth (15-3-2). Goalie Lauren Griffin eclipsed 200 career saves for King Philip, which advances to face their Hockomock rival, fourth-seeded Canton in the quarterfinals. Westwood 1, Masconomet 0 — After a scoreless deadlock through regulation, Ellie Harrington delivered the winning goal just 22 seconds into overtime on an assist from Bridget Hughes to power the No. 10 Wolverines (12-6-2) to a win over previously unbeaten No. 7 Masconomet (16-1-2) in second-round action. Division 1 State Andover 3, Bishop Feehan 0 — Senior Jessie Wang set the tone with 11 kills and six aces and senior Naomi Vajda added six kills and three blocks to propel the No. 4 Golden Warriors (18-4) to a sweep of No. 13 Bishop Feehan (15-7) in a second-round matchup. Division 2 State King Philip 3, Reading 0 — Cece Kilroy led the fifth-seeded Warriors (16-7) past No. 13 Reading (16-7) with 7 kills, 12 digs, and 3 aces. Senior captains Shayne Dugan (12 kills), Caleigh Shore (16 digs), Cece Mullen (5 aces) contributed, and Molly Sweeney (5 kills) and Mya McCormick (4 aces) chipped in. King Philip awaits the winner of No. 1 Oliver Ames and No. 9 Canton in the semifinals. Globe correspondents Matty Wasserman, Toby Moses, and Alexandria Evans contributed to this report.