Jared McCann nearly cut the deficit to one goal on a power play at 5:43 of the third period, sending a shot off the left post from the left face-off circle.
Crosby scored an empty-net goal at 17:39 of the third for the 3-0 final, his 26th goal of the season. He has scored at least 25 goals in 14 of his 19 NHL seasons.
Defenseman Vince Dunn, who leads Seattle with 35 points (eight goals, 27 assists) in 42 games, did not play because of an undisclosed injury.
Adam Larsson, Dunn's partner on the top pair, left because of an illness after playing 4:01 in the first period, leaving the Kraken to finish the game with five defensemen.
"You've got five guys to go play," Seattle coach Dave Hakstol said. "Those guys did a pretty good job. Our [defensemen] did a pretty good job, the five guys that were in tonight. We didn't manage the puck well enough up front."
NOTES: Kraken forwards Matty Beniers (undisclosed) and Andre Burakovsky (lower body) did not play after each was injured Saturday. Beniers, Burakovsky, Dunn and Larsson are day-to-day, Hakstol said. ... Pittsburgh defenseman Chad Ruhwedel left at 11:06 of the third after taking a hit from Seattle forward Eeli Tolvanen, who was called for boarding. There was no update after the game. ... Penguins forward Noel Acciari had three hits in 14:05 of ice time after being a game-time decision because of an upper-body injury that kept him out of a 3-2 overtime loss to the Carolina Hurricanes on Saturday. ... It was Crosby's 458th multipoint game, passing Phil Esposito for 10th all-time.