Morrissey snapped a 3-3 tie with 6:10 left in the game to give Winnipeg a 4-3 lead. Forward Kyle Connor, who assisted, added an empty-net goal at the buzzer.
Dominic Toninato, Pierre-Luc Dubois and Blake Wheeler also scored for Winnipeg, which improved to 22-18-8. Goalie Eric Comrie stopped 20-of-23 shots for the win at Canada Life Centre. Dylan DeMelo had two assists.
Vince Dunn, Marcus Johansson and Jordan Eberle scored for Seattle, which fell to 16-30-4. Kraken goalie Philip Grubauer made 24 saves on 28 shots.
Morrissey converted a perfect pass from Connor and beat Grubauer cleanly for the game-winner. Forward Kristian Reichel also assisted.
Seattle tied the score 3-3 7:02 into the final frame. Forward Eberle tipped in a pass from forward Johansson from the crease.
Jets captain Wheeler, who had two points, gave Winnipeg a 3-2 lead at 11:54 of the second period when he converted a pass from Paul Stastny from alone in front. Stastny stole the puck in the corner and immediately fed Wheeler.
The Jets knotted the score at 2-2 early in the second. Just getting out of the penalty box, Dubois fired a sharp-angled shot that beat Grubauer 1:45 into the middle frame. Wheeler made a good pass to put Dubois in the clear.
The Kraken took a 2-1 lead into the second period. Winnipeg cut into a 2-0 deficit when Dominic Toninato scored a short-handed goal with just 13 seconds left in the opening period. With Dubois off for high sticking, Toninato converted a perfect pass from centre Adam Lowry into an open net with Grubauer pulled out of position.
Seattle had jumped out to a 2-0 lead. With Winnipeg defenceman Logan Stanley off for boarding, defenceman Dunn fired a slapshot from the point that beat a screened Comrie just 3:21 into the game.
The Kraken followed that up when forward Johansson beat Comrie from the slot at the 12:15 mark.
It was the third of a four-game homestand for Winnipeg, who host the Edmonton Oilers on Saturday afternoon.
The Kraken will face the Flames in Calgary on Saturday, then wrap up a three-game road trip in Vancouver on Sunday night.
NOTES: The Jets played without veteran forward Andrew Copp, who suffered an undisclosed injury on Wednesday. He was replaced in the lineup by Kristian Vesalainen. â¦ Former Jets forward Mason Appleton played his first game in Winnipeg since the Jets left him unprotected in the NHL expansion draft. He had five goals and 13 points heading into Thursday night's match.