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.
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. 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.
Lucic and Patrice Bergeron added empty-net goals in the final 1:03 to cap off the scoring.
Frans Nielsen got the Islanders even at 1 in the second period with a short-handed, penalty-shot goal.
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.
Nielsen had tied it earlier in the period after he was awarded a penalty shot because he was tripped by Patrice Bergeron during a breakaway.
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.
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 Islanders have scored two goals or fewer in 15 of 17 games.
Notes: 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.