Crosby had a goal and two assists, all on the power play, for his second straight three-point game and the Penguins beat the Maple Leafs 5-2 on Saturday night.
"(We) had a long summer, had a lot of time to think about last year," Crosby said. "We're all pretty excited to get started. I think everybody's excited to get started, but it's nice to see it translate into a couple wins."
The line of Crosby, Hornqvist and Kunitz finished with six points and the Penguins went 3-for-5 on the power play. Crosby had two goals and an assist in the Penguins' season-opening win over Anaheim.
Joffrey Lupul and Tyler Bozak scored for Toronto. The Maple Leafs lost their home opener 4-3 to Montreal on a late goal Wednesday night.
"We have to find our game," Maple Leafs captain Dion Phaneuf said. "The bottom line is we have to be a lot better. Tonight, we got beat in all aspects of the game. They were harder on pucks, they were better in their special teams than we were.
Toronto's James Van Riemsdyk and Pittsburgh's Simon Despres had a brief fight with 33 seconds remaining.
Pittsburgh, which led 3-0 after the first period, outshot Toronto 41-25.
Leafs scoring star Phil Kessel's sluggish start continued with three trips to the penalty box, although one was a bench minor for too many men on the ice.
Hornqvist opened the scoring at 6:44 on Pittsburgh's second shot, pouncing on Christian Ehrhoff's shot from the point that bounced back off the end boards and firing a shot through Jonathan Bernier's legs.
There was more of the same at 7:44, 14 seconds into Kessel's hooking penalty. Kris Letang's shot from the point flew just wide of the left post and bounced off the boards behind the goal back out past the right post where a cruising Crosby beat Stephane Robidas to the puck and slapped it in.
Kunitz, camped in front of goal with two Leafs in the box, made it 3-0 at 17:46 when he redirected a Crosby's feed from near the side boards.
NOTES: The game was first of 18 sets of back-to-back games for the Leafs. They play Sunday in New York against the Rangers. Toronto was 13-18-1 in back-to-back games last season ... Pittsburgh defenseman Scott Harrington did not play after being recalled Friday from Wilkes-Barre/Scranton of the AHL.