Fleury silenced his critics for at least one night, making 27 saves in his 250th NHL win. He had one shutout in 33 games last season.
"I'm happy to get a win," Fleury said. "It's a long season though. This first one is done and I'm looking forward to playing the next one. The guys did a great job. They helped me out a lot and blocked some shots and covered the guys in front."
Penguins coach Dan Bylsma said he expected this performance from Fleury, despite his struggles in the Stanley Cup Playoffs last season.
"It was certainly a good start," Bylsma said. "I think early on in the game, there was not a lot of action for him and around him, but in the second period they started taking the play to us and he had to make a couple big saves."
Two defensive-zone breakouts led to Pittsburgh's first-period goals. Beau Bennett pushed the puck through the neutral zone to Kobasew, who dumped it to Brandon Sutter near the right boards. Sutter fired a snap shot into the middle of Cory Schneider's crest, and Kobasew pounced on the rebound and slid a shot into the net at 9:26.
Kobasew signed a one-year contract with Pittsburgh on Wednesday after working on a tryout through training camp. He performed well next to linemates Bennett and Sutter.
"I think we all bring something different," Kobasew said. "Beau is very skilled. [Sutter] is a great big body, two-way centerman, and I'm just trying to get in there, hunt pucks, be physical and get the puck to those guys."
Crosby scored 1:53 later on a 2-on-1 alongside Pascal Dupuis and facing defenseman Peter Harrold. Crosby teased a pass to Dupuis, who got his 200th career assist, before roofing a wrist shot past Schneider's glove.
Adams, in his 800th NHL game, scored with 8:18 left in the third period.
"It was a fantastic save that he made with the flash of the leg there," Bylsma said. "He played extremely well and earned his 250th win and the shutout tonight."
Crosby said he couldn't have envisioned a better way for Fleury to start the season.
"We believe in him," Crosby said. "I don't think there's any doubt in here. He made some great saves and we probably made him work harder than he needed to at the end, but those saves were beauties. So it's good to see him get the shutout and start it off with a win."
Schneider, the first goalie not named Brodeur to start New Jersey's season opener in 18 years, performed well for most of the game but was disappointed in his first period.
"It wasn't the best start from me," Schneider said. "It's tough to go down 2-0 to a team like that and have to claw back, but my teammates worked really hard in the second and third periods there, didn't give them a whole lot and we had a couple good chances, but Fleury made some big saves. So, [it was a] disappointing start all around."
Devils coach Peter DeBoer said Schneider played well enough for New Jersey to win, but the team couldn't capitalize in the second and third periods, when the Devils outshot Pittsburgh 22-9, for a 27-21 game total.
"I thought he was solid," DeBoer said. "It was the first game for a lot of guys. I thought the first period for all of us was a little slow. If it's to be expected, I don't know, but that was the difference in the game.
"I thought we were the better team in the second and third. We just couldn't finish."
Martin Brodeur will take over in net when the Devils face the New York Islanders on Friday at Prudential Center.
Pittsburgh's offense started to struggle when forward James Neal left the game after playing 3:49. He didn't take part in the morning skate and was listed as a game-time decision with an upper-body injury.
Bylsma said Neal was taken out in order to avoid aggravating his injury further and he will be evaluated Friday. The coach said if Neal misses any action, Bennett will skate in his place.
Thursday, Bennett and Adams filled in next to Evgeni Malkin and Jussi Jokinen, who replaced Neal on Pittsburgh's top power-play unit. The Penguins did not get credited with a shot on their only power play and cleared the puck themselves twice.
Schneider benefited from Pittsburgh's willingness to smother the puck in its end to hold on to its early lead.
Fleury recorded the shutout but barely had to face any true scoring chances until late in the third period. Robert Bortuzzo and Niskanen were especially effective shutting down New Jersey's forwards with Kris Letang out of the Penguins lineup.
Devils forward Damien Brunner was credited with eight shots; Henrique had three, and no other Devils player had more than two.