David Perron and Eric Fehr had the other goals for Pittsburgh (8-4-0), while Phil Kessel added two assists as the Penguins won their fifth straight.
Daniel Sedin and Jannik Hansen replied for Vancouver (6-3-4), which got 20 saves from Ryan Miller.
With the Penguins up 1-0 through 40 minutes, Crosby scored on a 4-on-3 power play after taking a nice feed from Kessel in front and beating Miller on a slick backhand at 7:17. The Pittsburgh captain came in with just one goal and four assists on the season and had been held off the scoresheet in nine of Pittsburgh’s first 11 games.
The Penguins then made it 3-1 just 2:55 later on a short-handed rush when Fehr walked around Canucks defenceman Yannick Weber on a delayed Vancouver penalty before roofing his second of the season.
Vancouver got one back at 13:59 when Sedin deflected Matt Bartkowski’s point shot past Fleury for his fourth.
The Canucks made it 3-2 with 67 seconds left in regulation when Hansen ripped his third of the year, but that would be as close as they got.
Down 1-0 after the first period, Vancouver had a great chance to even the score a minute into the second when Canucks defenceman Alexander Edler sprang Hansen on a breakaway. He moved in alone on Fleury, but his shot glanced on the goalie’s glove before hitting the post and staying out.
Fleury was at it again later in the same shift, flinging his body in front a Brandon Sutter shot from the slot with Vancouver buzzing in the Pittsburgh zone.
The Penguins then had an opportunity of their own with under eight minutes to go in the period, but Kessel’s shot off a feed from Evgeni Malkin rang off the crossbar behind Miller, with the puck somehow making it all the way into the Penguins’ bench off the carom.
The Penguins opened the scoring 4:53 into the first period after some sustained pressure in the Canucks’ zone when Brian Dumoulin’s shot from the point was tipped in by Perron for his first of the season.
Horvat had a chance to tie the score a few minutes later on a short-handed 2-on-1 rush with Hansen, but Fleury made the save from in tight.
Notes: The Canucks, who are 4-0-1 away from home, open a season-long seven-game road trip on Saturday in Buffalo against the Sabres. Vancouver next plays at Rogers Arena on Nov. 21 against the Chicago Blackhawks. … The Penguins visit the Edmonton Oilers on Friday. … Canucks forward Chris Higgins returned to the lineup after breaking his foot Vancouver’s first pre-season game.