Josh Bailey and Jean-Gabriel Pageau each had two assists for the Islanders, the No. 4 seed in the MassMutual East Division. Semyon Varlamov made 23 saves and won four of five starts in the best-of-7 series to help New York advance to the Stanley Cup Semifinals.
"Brock just had a child the other day with his wife, so he's been dealing with that," Islanders coach Barry Trotz said. "Game 4 (4-1 win on Saturday), he played that night with no sleep. He's been battling through that. … I think today, you saw him fresh. He settled in and played a Brock Nelson game."
New York has trailed 2-1 in each of the first two rounds of the Stanley Cup Playoffs. It also rallied to win three in a row against the Pittsburgh Penguins.
"Whenever you have an opportunity to close a team out, you want to bring your best and I thought we've been able to do that both times now, against Pittsburgh and now Boston in front of great fans, great atmospheres," Nelson said. "It just feels right. You need to bring your A-game, and I thought we were able to do that again."
The Islanders will play the Tampa Bay Lightning, the No. 3 seed in the Discover Central Division, in the third round for the second straight season. The start of that best-of-7 series is to be determined.
Brad Marchand scored twice, and Tuukka Rask made 23 saves for the Bruins, the No. 3 seed in the East. They have lost in the second round two straight seasons after reaching the Stanley Cup Final in 2019.
"It's disappointing," Marchand said. "We expected a longer run in this room. We felt like we had a group that could go really deep this year. I think that it just came down to a couple of breaks. They capitalized on a few opportunities that they got, and we didn't on the other end. So I think there's some games that we really outplayed them and came up short, but that's playoffs."
Travis Zajac gave the Islanders a 1-0 lead at 8:52 of the first period on the rebound of Noah Dobson's shot from the point.