Tavares got even against Crosby and the Penguins, scoring his first game-winning goal with 6:12 remaining in leading New York to a 3-2 victory on Friday.
Tavares' rebound goal from the right post was his 10th goal of the season to cap an Islanders' two-goal rally in the final period. That marked the first time in 11 games New York won when trailing after two periods.
"It's nice to contribute when it matters most but overall it was a great team effort," Tavares said. "It starts from everyone and to cash in there was a bonus."
Josh Bailey and Sean Bergenheim added goals and Dwayne Roloson made 19 saves and New York scored two goals in the final period for its second win in three games.
Evgeni Malkin and Matt Cooke scored for Pittsburgh and Brent Johnson made 34 saves.
The Islanders killed off five power plays, including a key second-period 5-on-3, in snapping Pittsburgh's three-game winning streak.
Roloson has 77 saves in the past two games after stopping a regular-season franchise-record 58 shots against Toronto earlier this week.
"We came out in the third and played phenomenal," Roloson said. "It was the best period of hockey we've played. I give our guys credit for shutting down some very talented offensive players."
New York entered the game 0-7-3 when trailing after two periods. But Bergenheim and Tavares each scored in the final period to end the streak. Pittsburgh entered 11-1 when leading after two periods.
"We pride ourselves on being a strong third-period team and raising our level when it's time and we didn't do a good job of it tonight," Crosby said.
Two days after mustering one third-period shot in a loss to Philadelphia, the Islanders had 18 third-period shots in outshooting the Penguins 37-21 for the game.
"We pushed the pace and we generated some really good chances in all periods," Islanders coach Scott Gordon said.
Tavares' first goal in five games came off a good bounce after Johnson stopped Freddy Meyers' point shot. The No. 1 overall pick in the draft was left open right outside the crease and buried the rebound chance for the win against the division rival.
"It was bouncing and I wanted to make sure I got enough wood on it," Tavares said. "It's big to get a game like this. It's almost like a four-pointer."
Crosby had 12 goals and 28 points through his first 26 career games. Tavares has 10 goals and 21 points through the same point and Crosby said the 19-year-old center has improved since the last time he opposed him.
"From what I've seen, even from the first game, he's looked pretty comfortable out there," Crosby said. "It's a confidence thing. You have to believe the things you do will work."
Mark Streit helped generate New York's first goal with a spin move at the left point before firing a hard shot. Johnson made the initial pad save before an open Bailey slammed home the rebound at 9:05.
Malkin scored almost seven minutes later when he moved past Bailey and fired a sweeping backhand from the low right circle with 2:38 left in the period. Roloson skated deep in his net to cut off the angle but Malkin's shot still squeezed in for his seventh goal.
Pittsburgh took the lead 7:12 into the second off Cooke's rebound goal. Roloson made a right pad save on Jordan Staal's top-of-the-circle wrist shot before Cooke skated past Streit and tapped-in the second chance for his fifth goal.
Bergenheim's left circle wrist shot beat Johnson on the glove side to tie it 2-all at 1:24 into the third before Tavares' clinching goal.
"Everything to this point that the Islanders have done this year has proven they are a hardworking team" Penguins coach Dan Bylsma said. "In the second and third, they put us in the 'D-zone' and tired us out tonight."
A struggling Pittsburgh power play prevented the Penguins from extending a 2-1 lead late in the second period. The Islanders killed off a 55-second, 5-on-3 chance after Andy Sutton was called for a high-sticking double-minor at 14:24. New York allowed just three shots during the nearly five-minute short-handed stretch.
"Clearly [that was] an opportunity that we did not capitalize on and they were energized by dodging that bullet and kept coming pretty hard after that," Bylsma said.
Pittsburgh's power play has converted just 4 of 55 chances over the past 14 games. The Penguins will face the Rangers at home on Saturday night.
Holiday cheer didn't extend much beyond the opening faceoff as Tim Jackman and Deryk Engelland fought near center ice 13 seconds in ... The Islanders wore white jerseys at home for the first time this season while Pittsburgh wore its alternate powder blue uniforms ... Pittsburgh's Tyler Kennedy (groin) and defenseman Kris Letang (shoulder) practiced Thursday but did not play ... After being scratched Nov. 13 for the first time in his NHL career, Bailey has four goals in his past five games.