Horvat scored 32 seconds into the second period on a power play to make it 2-0, but Rakell cut it to 2-1 on a power play at 16:03, tapping in a loose puck in the crease after Martin stopped Bryan Rust's shot from the slot.
Kuzmenko restored Vancouver's two-goal lead, deflecting a Luke Schenn point shot to make it 3-1 at 10:28 of the third.
"Confidence is an amazing thing," Boudreau said, "And it looks like we're gaining a little bit right now."
Horvat pushed it to 4-1 at 16:42 on a power play, tipping in an Oliver Ekman-Larsson point shot for his team-leading sixth goal, and J.T. Miller scored into an empty net during a 5-on-4 at 17:50 for the 5-1 final.
"Obviously there's a lot more energy, obviously the smiles on our faces," Horvat said of the feeling in the locker room. "But we've got to dig ourselves out of the hole here. Obviously, we put ourselves in this situation. Just because we won two games, you can't be satisfied. We've got to keep going here."
Martin, who hasn't lost in regulation in two seasons with the Canucks (4-0-4) and is 1-0-1 this season, stopped Rakell on a breakaway at 6:13 of the first and made a sprawling save on a rebound attempt by Crosby at 8:14 of the second on a power play.
"It probably feels good for everybody, but especially me, just to get my season started off in a good way," Martin said.
NOTES:Pittsburgh forward Jake Guentzel missed his fourth game after he was hit in the ear on a shot from Penguins defenseman Kris Letang in a 6-1 loss to the Los Angeles Kings on Oct. 20. … Penguins forward Jason Zucker missed his second game with an undisclosed injury. … Vancouver forward Jack Studnicka, who was acquired Thursday from the Boston Bruins, took part in warmups but did not play. … Defenseman Ethan Bear was acquired from the Carolina Hurricanes on Friday and is expected to join the Canucks on Saturday.