Zdeno Chara scored the tiebreaking goal early in the third period, Hamilton had two assists, and Tuukka Rask made 24 saves in the Bruins' 4-2 win over the New York Islanders on Friday night.
Patrice Bergeron, Shawn Thornton and Gregory Campbell also scored for Boston, which improved to 3-0-1.
But it was the 19-year old Hamilton who brought chants of "Doug-ie! Doug-ie!" echoing around TD Garden late in the game.
"I was just trying not to fumble the puck," said Hamilton, who broke into a smile while surrounded by reporters as he sat at his locker. "It's obviously nice to hear the support. It's pretty cool."
When the season started, Boston had six games to decide to keep him or send him back to juniors. The experiment might be complete.
"I think that's why our guys drafted him," Boston coach Claude Julien said. "Those are the kinds of things we saw in him. We're pretty happy with what he's done."
Hamilton assisted on Boston's first and final goals of the game.
"It's great," Rask said of the chants. "He's such a great player. He's just going to get better."
Hamilton isn't even over the fact that he is playing in the NHL.
"It feels so weird being out there instead of watching it," he said.
New York's Keith Aucoin had his first career two-goal game, and has scored three times in two games.
Rick DiPietro, playing his first game since Dec. 3, 2011, after last season was cut short by a groin injury, made 23 saves for the Islanders.
"I felt good," said the former Boston University star, who was the No. 1 overall pick in the 2000 NHL draft. "It's always exciting playing back here in Boston, and I always look forward to playing in this building. I was excited."
New York (2-2) played the second of five straight on the road after ralling to beat Toronto 7-4 on Thursday night.
"For the most part we were up to the challenge, but couldn't get it done," Islanders coach Jack Capuano said.
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The game featured a matchup of the NHL's best two penalty-killing units this season. The Bruins have turned aside all 17 short-handed situations, and the Islanders improved to 13 for 13.
Rask has played in all of Boston's games.
Boston took a 3-2 lead 7:07 into the third when Milan Lucic circled from behind the net and fed Chara, who fired a wrist shot past DiPietro's glove inside the left post from the high slot.
Bergeron scored on a breakaway with 6:27 to play, shifting a few times before tucking in a forehand shot.
Chara hit the left post in the closing minute with a backhand shot from the blue line after the Islanders pulled DiPietro for an extra skater.
The Bruins grabbed a 1-0 lead 4:52 into the game. Thornton, benched Wednesday for a good portion of Boston's 4-3 overtime loss at the New York Rangers after a giveaway led to a goal, backhanded in the rebound of Hamilton's shot from the left point.
New York tied it on Aucoin's goal midway into the period. Aucoin came charging into the slot and redirected Colin McDonald's pass from behind the net past Rask.
Aucoin got to an errant clearing attempt in the high slot and unloaded a slap shot past Rask's glove to give the Islanders a 2-1 edge midway into the second, but the Bruins tied it less than 4 minutes later. Campbell controlled a rebound in front and put the puck past DiPietro.
NOTES: New York LW Matt Moulson played in his 250th straight game. He hasn't missed a game with the Islanders. ... Boston D Dennis Seidenberg, who missed two games because of an undisclosed lower body injury, returned. ... The Islanders will play at Winnipeg on Sunday. ... The Bruins are off until Monday when they play at Carolina. ... Boston is 15-3-1 in its last 19 games against New York. ... Boston went 0 for 3 on the power play, dropping to 1 for 17 this season. ... It was the second straight night a team from New York played at TD Garden. The NBA's Knicks beat the Celtics on Thursday.
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