Morgan's tally sparked a three-goal, third period outburst by the Jets in just under a five minute span that broke the game wide open for a Winnipeg side that spotted the visitors a two-goal lead.
Saku Maenalanen, Dylan Samberg, Mark Scheifele also scored for Winnipeg, who bounced back after a 4-1 loss to the Columbus Blue Jackets on Friday.
Defenceman Nate Schmidt had a goal and an assist.
Adam Lowry had a pair of assists for the Jets.
Connor Hellebuyck turned aside 28 shots for Winnipeg, who moved to 15-7-1.
Jakob Silfverberg and Brett Leason scored for the Ducks, who lost their 6th straight game.
Anthony Stolarz made 35 saves for Anaheim, who dropped to 6-17-3.
Jakob Silfverberg opened the scoring 15:16 into the first when he snapped up a rebound off a Frank Vatrano shot to make it 1-0 Anaheim.
Brett Leason made it 2-0 just over five minutes into the second when () won a draw back to Dylan Samberg, who had the puck hop over his stick at the point.
Leason skated into the disc and broke in alone on Hellebuyck, beating him with a wrister to score his 2nd goal of the season.
"Well it just kind of came to me. That defence (Samberg) lost the puck off the draw and I kind of stepped and it was there. I was able to get a breakaway and was able to capitalize," said Leason.
"I was playing man to man for my position, just a fortunate bounce for me and I hopped on the opportunity," he added.
Saku Maenalanen got the Jets on the board 10:31 into the second when he converted a Nate Schmidt feed from the side of the net to make it 2-1.
The goal was his 4th of the season.
Dylan Samberg scored 13:28 into the second when he floated a wrister through traffic from the left point which beat Stolarz glove side to make it 2-2.
The goal was the first of his NHL career.
The goal was challenged by Anaheim for a high stick but was allowed to stand.
Morgan Barron gave Winnipeg the lead at 14:23 when he got his stick down after driving the net and slammed an Adam Lowry feed past Stolarz to make it 3-2 Jets.
Mark Scheifele followed up with a goal 49 seconds later at 15:12 when he took a drop pass from Blake Wheeler just inside the Ducks blue line before moving in nad wiring a wrister past Stolarz, beating him high glove side to make it 4-2 Jets.
The goal was his 13th of the season.
Nate Schmidt scored a late power play goal off a wrister from the point to make it 5-2 Winnipeg.
But Jets Head Coach Rick Bowness didn't make any bones about how his club started the game, he wasn't happy.
"Good or bad, I don't look at it that way. It's just not right to start a game like that. Listen, I'm the head coach so I'm responsible for the way we start and getting our team prepared. So that starts with me. The second thing is I'm not a babysitter. These guys are men. They're professionals and they're paid to show up here and go to work. My job here is to make that happen. The third thing on that would be: you cannot play this game without passion. Without emotion. You cannot play this game on your heels. And I hate when we're on our heels. It's not right."
Anaheim Head Coach Dallas Eakins said his club played hard but couldn't match the Jets.
“It's hard. You're coming into a game like this, you know your backs are going to be against the wall anyway. Winnipeg had just lost a tough one (to Columbus Friday) and we're playing back-to-back and they're sitting here fresh so you know it's going to be a tough game," said Eakins.
“I thought our guys did a hell of a job throughout the game, leading early and hanging on. The winning goal just comes off of a guy. Our D-man got his feet tangled up with another guy and he falls. If he doesn't fall, we're probably right now in overtime or a shootout.”
Winnipeg closes out a four-game homestand Tuesday when they host Florida while Anaheim returns home to face the Carolina Hurricanes.
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