Tanner Jeannot also scored, and Fraser Minten had two assists for the Bruins (14-11-0), who won the final two games of a four-game road trip (2-2-0). Jeremy Swayman made 39 saves.
Boston is 3-0-0 against New York this season.
Mathew Barzal scored the lone goal for the Islanders (13-9-2), who have scored just two goals in the first three games of their seven-game homestand (1-2-0). Ilya Sorokin made 11 saves.
Barzal gave the Islanders a 1-0 lead at 4:41 of the first period. He received a pass from Tony DeAngelo in the left circle, made a move around Pavel Zacha, and pulled Swayman out of position along the goal line before reaching back and tucking the puck behind the goaltender at the left post.
Steeves quickly responded at 6:23 to tie the game 1-1. Sean Kuraly’s centering pass hit off the skate of Adam Boqvist and landed right on the stick of Steeves, who tapped it into the open net from the edge of the crease.
Simon Holmstrom had a wrist shot trickle past Swayman at 17:50, but Bruins defenseman Hampus Lindholm was able to swipe the puck under his goaltender before Max Shabanov could jam it in.
Jeannot gave the Bruins a 2-1 lead 43 seconds into the second period. He controlled a loose puck near the right hash marks and roofed a shot over Sorokin’s glove.
Steeves scored a short-handed goal to extend the lead to 3-1 at 10:21 of the third period. Minten skated in on a 2-on-1 rush and toe-dragged around a sliding Matthew Schaefer before passing over to Steeves for a one-timer in front.
New York is 0-for-23 on the power play in its past seven games.