Greaves made 19 saves in a 5-4 overtime loss at the Edmonton Oilers on Monday.
Adam Fantilli scored for the Blue Jackets (8-7-1), who received goals in the shootout from Kirill Marchenko and Charlie Coyle.
Ryan Winterton scored and Matt Murray made 33 saves for Seattle (7-4-5), which has lost three of four.
Winterton scored his second NHL goal in his 37th game to give the Kraken a 1-0 lead at 16:43 of the first period.
Ben Meyers stole the puck from Denton Mateychuk with a hit along the wall in the Columbus zone. Meyers drove to the right post before backhanding a pass back to Winterton, who scored with a one-timer from the left hash marks.
Winterton scored his first NHL goal on Nov. 5 in a 6-1 loss to the San Jose Sharks.
Eeli Tolvanen tripped Greaves while he was playing the puck behind the net and Ryan Lindgren cross-checked Fantilli into Murray 53 seconds later, giving the Blue Jackets a 5-on-3 power play.
Murray lost his stick during a scramble in front of the net and was on his side in the crease when Fantilli shot the loose puck off the goaltender’s glove and into the net from the inside edge of the right circle to tie it 1-1 at 18:22.
Marchenko assisted on the goal to extend his point streak to an NHL career-high nine games (11 points: three goals, eight assists).
Columbus captain Boone Jenner went to the locker room early in the second period with an upper-body injury and did not return.