The Islanders got four of their 12 first-period shots during that power play and got even when Nielsen netted his 18th goal with 4:31 left.
New York started the second period on the power play after Chara took a penalty for throwing a retaliation punch at Cal Clutterbuck.
The Islanders answered again, taking advantage of a turnover in the Boston zone by Gregory Campbell. During a delayed penalty, Okposo made a pass into the middle to Grabner for his ninth goal and second in three games, scored at 8:20.
“That power play really gave them momentum, and we finished on our heels in the first,” Bruins coach Claude Julien said. “From that point on until the end of the second period, I thought we got really sloppy and shot ourselves in the foot.”
The Bruins went ahead 3-2 at 12:21 during another delayed penalty. Shawn Thornton’s pass hit New York’s Matt Martin and caromed to Smith, who tapped in his 17th goal.
Another Bruins breakdown cost Boston the lead again. Defenseman Dougie Hamilton leaped at the blue line to knock down a puck, but missed. The speedy Grabner took off and was joined by Okposo, who came out of the penalty box.
They came in on a 2-on-0 break and passed the puck back and forth before Okposo slammed in his 23rd goal with 4:52 left.
It appeared the teams would be tied to start the third, but Soderberg steamed in on the right wing, got around defenseman Thomas Hickey and beat Poulin with 32.7 seconds remaining.
“We can’t panic,” said Islanders captain John Tavares, who had a six-game point streak snapped. “Have to trust each other in this room.”
NOTES: Okposo has seven goals and eight assists since his daughter was born earlier this month. … The Islanders activated D Lubomir Visnovsky off the injured list. … Rask is expected to start Tuesday when the Bruins host Florida.