Morrissey took a pass from Mark Scheifele and fired a high shot past goalie Cam Talbot for his fourth goal of the season.
The Jets have won three straight, while Edmonton’s win streak ended at four games.
Scheifele, Mathieu Perreault, Nikolaj Ehlers and Patrik Laine also scored for Winnipeg. Dustin Byfuglien, Bryan Little and Blake Wheeler each contributed a pair of assists. Byfuglien has one goal and five assists in a three-game point streak.
Connor Hellebuyck made 22 saves for the Jets (20-9-2), who finished off a four-game homestand going 3-1-0. Talbot stopped 35 shots for the Oilers (17-12-3).
Ryan Spooner, Darnell Nurse, Jujhar Khaira and Alex Chiasson replied for the Oilers. Chiasson added one assist and Leon Draisaitl had a pair.
McDavid also picked up two assists, extending his point streak to seven games with four goals and nine assists. He also reached 301 career points in 240 games.
Draisaitl stretched his point streak to four games with three goals and six assists.
After the Oilers scored three straight goals in the second period to make it 4-3, Scheifele tied it at 9:58 of the third with his 18th goal of the season. Winnipeg kept attacking, outshooting Edmonton 17-2 in the third.
Connor McDavid hit the post just before Morrissey’s goal.
Spooner opened the scoring at 10:12 of the first after Draisaitl intercepted a Jets pass attempt and sent the puck to him in the slot for a low one-timer that beat Hellebuyck.
Perreault scored on the power play with a backhand shot at 15:43. Ehlers was credited with a goal 68 seconds later when his shot went off the skate of Edmonton defenceman Kevin Gravel.
Laine notched his 22nd goal of the season, and first in seven games, after Byfuglien sent the puck to him in the slot. His shot hit Talbot and bounced into the net at 1:42 of the second period to make it 3-1.
Nurse started the visitors’ three-goal run at 6:04 with a rebound that went off his skate. Khaira’s goal was a redirect of a wraparound by Jesse Puljujarvi at 17:18. Chiasson scored seven seconds into a power play at 18:55 when he redirected a McDavid pass.
Wheeler set up the tying goal, feeding a pass from behind the net out to Scheifele, who quickly flipped the puck by Talbot at 9:58.
Winnipeg plays in Chicago Friday, while Edmonton hosts Philadelphia on Friday.