Vanek, the left wing acquired from Buffalo for fan favorite Matt Moulson, scored his first goal with the Islanders and recorded his 500th NHL point.
The scoring play came on a perfect cross-ice pass from right wing Kyle Okposo. Vanek finished it with a one-timer from the left circle past goalie Chad Johnson.
"That felt really good, a relief for me," Vanek said. "Each day we're feeling better and better and working together. Tonight you saw what can be possible with our line."
Tavares knocked a loose puck past Johnson at 6:15 of the second for his sixth goal of the season. The assist went to Vanek.
After MacDonald scored his first of the season at 13:13 to make it 2-0, and Boston's Dougie Hamilton answered two minutes later, Vanek notched his 255th NHL goal.
"He's a great skilled player," Tavares said. "When you get those opportunities, you have to take advantage of them, and he did. When we play our game and compete, we are successful."
Okposo and defenseman Travis Hamonic assisted on the goals by MacDonald and Vanek.
The Islanders (6-5-3) won for the second straight night. On Friday, they bombarded the Ottawa Senators with 57 shots and won 5-4 in a shootout, twice rallying from two-goal deficits.
"Our last six periods have been very good," Islanders coach Jack Capuano said. "Kevin was particularly solid for us tonight. This was a strong character win."
Tavares, who has played 221 consecutive games, seemed more at ease with the new line combination of Vanek and Okposo. Moulson had been Tavares' left wing and close friend since the captain's rookie season in 2009-10, scoring 118 goals for the Islanders.
Boston (8-5) lost for the third time in four games.
He also stopped Milan Lucic's backhand from in front with 1:29 left in the third as the Bruins had Johnson pulled for an extra skater. He made another glove save on Hamilton with 23 seconds remaining, sparking chants of "Pou-lin, Pou-lin" from the home crowd.
"I felt strong out there, working hard at doing the little things right," Poulin said.
The 23-year-old Poulin's two other starts in place of No. 1 goalie Evgeni Nabokov were losses -- 3-2 at Chicago and 5-2 at home to Philadelphia.
Johnson played his second game of the season to give Tuukka Rask a rest. Johnson won his only other start, 5-2 at Buffalo on Oct. 23.
The Bruins, coming off a 3-2 shootout win over Anaheim on Thursday, will start a five-game homestand against Dallas on Tuesday. They had won their previous three visits and eight of 10 at Nassau Coliseum.
"We weren't focused or sharp enough," Bruins coach Claude Julien said. "We'll be working hard to get the team back on track."
The Islanders will embark on a four-game trip starting Tuesday at Washington before they head to Carolina, Columbus and Montreal.