"I am taking advantage of my opportunities right now, and it's also nice to have a little luck," Lucic said. "It's a credit to my linemates. They are finding me when I am open."
Lucic leads the team in goals with 15, easily topping last season's total of nine.
Boston extended the Islanders' futility to 1-15-3 in their past 19 games. New York, which has lost 11 straight road games, hasn't won since beating New Jersey at home on Nov. 26.
The Islanders (5-16-5) are last in the NHL with 15 points.
"Finding a way to get up for these games is more challenging than you think, especially emotionally," Bruins defenseman Zdeno Chara said. "Give New York credit though. They played hard and battled back in the second."
Rask won for only the second time this season (2-6-1). Boston is 4-0-1 in its last five.
Brad Marchand scored a short-handed goal with 5:20 remaining in the second period for a 2-1 lead. Michael Ryder scored one of two power-play goals for Boston at 14:16 of the third period for a 3-1 lead before Rob Schremp narrowed the Bruins' lead to 3-2 with 3:33 remaining.
"Any time a team scores against us short-handed, it's a real kick in the butt. We want to make sure we do the same to them," Marchand said.
Lucic and Bergeron added empty-net goals in the final 1:03 to cap the scoring.
Marchand put the Bruins ahead 2-1 when he blocked a clearing attempt by Islanders goalie Rick DiPietro, who was well out of the crease, and slid the puck into an open net.
"We really battled hard and competed hard," New York's second-year forward John Tavares said. "This game was a tough one to swallow."
DiPietro made 32 saves for the Islanders, who were 0 for 3 on the power play. New York has failed in 39 straight advantages over 12 games.
"The frustration builds when you lose, period," DiPietro said. "It doesn't matter how close or how. One goal, 10 goals -- a loss is a loss."
Lucic's fifth goal in five games, a power-play tally, put Boston ahead 1-0 with 6 minutes left in the first. Marc Savard earned an assist for his first point of the season in his fourth game.
The Islanders have scored two goals or fewer in 15 of 17 games.
Boston recalled Steven Kampfer from AHL Providence to replace defenseman Mark Stuart, who is out four to six weeks because of a broken finger. ... The Islanders entered the game 18 points behind the final playoff spot in the Eastern Conference. ... Boston improved to 9-1-1 in its last 11 against New York. ... Islanders D Radek Martinek left the game in the first period after blocking Zdeno Chara's slap shot, but returned. Tavares was knocked out of the game by another slap shot by Chara with eight minutes remaining.