Vince Dunn tied it 1-1 with his own power-play goal at 10:44.
Donato gave Seattle a 2-1 lead at 16:04, taking advantage after Jordan Oesterle slipped and lost the puck in the Red Wings' zone, but Vladislav Namestnikov tied it 2-2 at 18:18 when his shot fluttered in off the glove of Grubauer.
Raymond scored his 10th of the season to put Detroit ahead 3-2 at 6:30 of the third. He got to a loose puck in the slot after Larkin's attempt was blocked and beat Grubauer under his right arm with a turnaround shot.
"It's great playing with [Larkin] because he's such a good player and he makes it easy to be out there with him," Raymond said. "He's been a huge help to me on and off the ice."
After Dunn hit the crossbar at 8:59, Donato tied it 3-3 at 14:16 with a shot from the right circle.
"I thought we had a couple really good stretches in the game, especially when we got behind in the third period and still found a way to earn a point," Kraken coach Dave Hakstol said. "That's something we've been able to do in this stretch."
Greiss kept the game tied by making a lunging save with his right pad on Yanni Gourde at 2:10 of overtime, and Filip Hronek hit the post with six seconds remaining on Detroit's only shot attempt of the extra period.
"Getting a point out of this game is massive," Gourde said. "We've got to be a little bit better than this, but we battled. We can play like this every night."
NOTES:The Red Wings played without forward Tyler Bertuzzi, who is unvaccinated and was placed in NHL COVID-19 protocol earlier Wednesday. Blashill said Bertuzzi is "feeling fine" but that he will remain in protocol for 10 days and miss Detroit's next four games. … The shootout was Seattle's first in its history. … Greiss' win was his 150th in the NHL. He is 150-111-36 in 327 games (290 starts) with the San Jose Sharks, Phoenix Coyotes, Pittsburgh Penguins, New York Islanders and Detroit.