Frans Nielsen and Jeff Tambellini scored shootout goals, and Joey MacDonald turned aside Penguins stars Evgeni Malkin and Sidney Crosby in the tiebreaker to snap the Islanders' 0-4-1 skid.
"I was a little bit surprised, but the team is struggling, so things can happen," captain Crosby said of the change. "The first time we met him was at a team meeting this morning, and then we went through our normal pregame routine."
Bylsma got the call that he would replace Therrien on Sunday, just before he was set to coach his Wilkes Barre-Scranton club in an AHL game.
The decision to dismiss Therrien, who led the Penguins to the Stanley Cup finals last year, was made by general manager Ray Shero after Pittsburgh blew a 2-0 lead at Toronto and gave up five goals in the third period of a 6-2 loss Saturday.
"When I talked to Ray Shero (Sunday), there were some nerves," Bylsma said. "But this was an opportunity you work for and if you are granted it, you do the best you can. I think with the little time we've had together, as the game went on, we got more in tune with the way we should be playing."
Bylsma is faced with the task of implementing a new fast, attacking style that can make the most of the Penguins' talented forwards. It produced a season-high 37 shots Monday, but only one point in the standings.
Malkin and Ryan Whitney scored tying goals, and Marc-Andre Fleury made 28 saves through overtime for the Penguins, 1-7-2 on the road in 2009. Pittsburgh (27-25-6) is 10th in the Eastern Conference, two places and four points below the playoff cutoff.
"We want two points every game, especially right now," forward Jordan Staal said. "The guys in the dressing room know what we're capable of. We know what we can do out there. It's a matter of going out and doing it."
Chris Campoli and Frans Nielsen scored for New York, which owns the NHL's worst record (17-33-6).
Bylsma paced behind the Penguins bench, keeping his arms folded for most of the game, and taking occasional drinks from a water bottle. He leaned over several times to talk to his new players. Only two Penguins in the lineup played under Bylsma in the AHL.
"He was right in the mix," Staal said. "In the third we really started to show what we could do in that system. Obviously we didn't get the result."
The Penguins erased a pair of one-goal deficits with 20 shots through two periods and then turned it on.
"We have to play that way for 60 minutes," Bylsma said. "If you do, you tip the scales in your favor."
A pretty passing play produced Whitney's second goal of the season and tied it at 2 with 2:53 left in the middle frame.
Sergei Gonchar, playing just his second game of the season, gave Pittsburgh's power play a lift with his first point. Gonchar moved the puck from the blue line to Crosby in the right circle, and the Penguins captain sent a backhander back toward the left circle to Whitney, who fired a rising one-timer past the sprawling MacDonald.
The Islanders had taken their second lead less than 4 minutes earlier. Nielsen crashed the net and pushed the puck past Fleury with his second backhanded swipe after Andy Hilbert's original shot trickled behind the goalie.
Nielsen's third goal snapped his 19-game drought at 13:26.
"It's great to get the win," MacDonald said. "We knew with the coaching change that they would come out hard, and we responded pretty good. You've got to bump your game up when you face those guys in a shootout, but it helps when you score on your first two shots."
New York, which had 19 shots through 40 minutes, went on its first power play early in the third period after Malkin was given four minutes for roughing following a scrum in front of MacDonald with 10 seconds left in the second.
Malkin, the NHL scoring leader with 82 points, threw a few jabs at Campoli - who drew only one penalty for roughing - and was dragged down from behind by Hilbert.
Campoli staked the Islanders to a 1-0 lead with 8:26 left in the first period, after Sean Bergenheim's pass hit Penguins defenseman Kris Letang in the leg and caromed in off the right skate of Campoli. The goal stood up after a video review because Campoli didn't kick the puck.
Malkin scored his 25th goal by stripping the puck from Campoli along the left-wing boards, racing into the Islanders end on a 2-on-1 with Petr Sykora, blowing by defenseman Jack Hillen, and beating MacDonald with 1:53 left in the first.
Notes: Bylsma was 35-16-1-2 with Wilkes-Barre/Scranton in his first season as an AHL coach. ... Whitney hadn't scored in 12 games. .. Campoli's goal was his first in 11.
