Satan scored on the Islanders' first shootout attempt and the Bruins extended it to sudden death when Marc Savard scored on the Bruins' third shot. Brad Boyes than failed to convert and Blake put a shot over the shoulder of Bruins goalie Hannu Toivonen for the game-winner.
Viktor Kozlov tied the game 4-4 for the Islanders with 1:39 remaining in regulation when he scored a power-play goal by sliding the puck past Toivonen.
The Islanders won for only the second time in the last eight games and in 20 games when trailing after two.
Paul Mara had provided the Bruins a short-lived 4-3 lead with 6:15 remaining in the game when he went around a helpless Sean Hill and slid the puck past Islanders goalie Rick DiPietro.
Boston has only one win in the last six and allowed three goals or more for the ninth straight game.
Tom Poti scored the Islanders second power-play goal to tie the game 3-3 with 10:29 remaining in the third. New York began the night 2-for-39 over its previous 10 games on the power play.
Zdeno Chara had given Boston a 3-2 lead when he scored on a slap shot from the point with 15:40 remaining.
Trent Hunter tied the game 2-2 for the Islanders 22 seconds into the third period when he flipped the puck past Toivonen.
Patrice Bergeron and Savard each scored in the opening 8:40 to put the Bruins ahead 2-0. Bergeron scored on a rebound of his own shot and Savard scored on a backhander while DiPietro was out of position.
Randy Robitaille cut the Bruins lead in half at 2-1 when he tipped a shot by Satan beating Toivonen 5:39 into the second period.
P.J. Axelsson and Savard had two assists each for the Bruins.
Notes: Chara scored his 200th career point on a first period assist. . . . Alexei Yashin had an assist to extend his four-game point streak and has 44 career points in 48 games against Boston. . . . The Bruins had been outscored 28-9 in the last five games. Savard has nine points in the last five games.