Ben Kindel then pushed it to 5-1 by deflecting a point shot from Karlsson on a power play at 15:32.
"Some good, some bad," said Kindel, who returned from missing the season opener with a lower-body injury. "Obviously, the first game coming back here, I felt like it kind of took a little bit to get going. But started making some plays, but still some stuff to work on as well."
Suzuki cut it to 5-2 at 18:46 on a backhand shot after splitting the defense.
Caufield pulled Montreal to within 5-3 with a wrist shot from the high slot at 3:31 of the third period.
Chinakhov seemed to extend the lead at 5:25, but the play was ruled offside after a challenge from the Canadiens.
"I think any game you're going to have things that you're going to look back on," Penguins coach Dan Muse said. "There's some more things to clean up after tonight, for sure."
NOTES: Malkin is the second 40-year-old in NHL history to score in each of his first two games of a season, joining Gordie Howe (1968-69). ... Crosby's assist on Girard's goal was his 1,109th in the NHL, tying Joe Thornton for seventh in League history. ... Caufield led the NHL with 21 goals in games that took place on Saturday night last season. ... Forward Andrei Kuzmenko made his Penguins debut after taking a leave of absence on Sept. 24 to mourn the death of his father, Alexander. Kuzmenko signed a one-year, $5 million contract with Pittsburgh on July 1. ... Montreal defenseman Alexandre Carrier left in the second period with an undisclosed injury. An update was not provided.