After Brock McGinn tied it 3-3 with a backhand at 4:53 of the third period, Crosby gave the Penguins a 4-3 lead by tapping in a pass from Rust at 7:10. Crosby has scored 32 points (10 goals, 22 assists) in his past 23 games after scoring two (one goal, one assist) in his first seven this season.
Letang scored his second of the game on a wrist shot, making it 5-3 at 11:36, and Brian Boyle scored by flicking a shot from between his legs for the 6-3 final at 13:42.
"We kept building," Letang said. "I thought we played a responsible game for 60 minutes. At the end, we got rewarded."
Schmaltz put the Coyotes ahead 1-0 at 8:23 of the second on a wrist shot from the right face-off circle.
Crosby set up Rust for a power-play goal that tied it 1-1 at 11:31 of the second. With his back turned, Crosby sent a pass between his legs to the left face-off circle, where Rust scored on a snap shot.
"Try to put it in the net, first and foremost," Rust said. "It's just one of those things you take a step back and say, 'That's another fantastic 'Sid' play.' I've been around for a while. I've seen a lot of those."
Keller gave the Coyotes a 2-1 lead with a wrist shot on a 5-on-3 power play at 16:22 of the second.