Ottawa's penalty kill provided the first goal of the game, as Nick Paul took advantage of a puck off the linesman in the neutral zone and fed Connor Brown to send him in alone. Brown snapped his fourth shorthanded goal of the season into the back of the net, beating Laurent Brossoit on the stick side with 8:29 left in the first.
Winnipeg's power play struggled to get traction early in the game, but while they finished 0-for-6 on the man advantage - the third straight game without a power play goal - the team did start generating better chances as the opportunities kept coming.
"The problem is we never got the goal that we needed," said Maurice. "We had the two or three shots, and the Dubois shots - that's the way it looks until you go bar-down on a guy.
"We just couldn't get it off the wall fast enough and then when we did we moved it around fine and couldn't get that shot through to the net that we needed to get through."
Winnipeg outshot Ottawa 17-4 in the second period, but still trailed by one heading into the final period.
Finally, during a stretch of four-on-four hockey in the third period, Morrissey and the Jets offence broke through.
Neal Pionk slid down the right side boards and sent a pass back to the middle of the ice, where Morrissey was waiting. He pinched his way down and sent a wrist shot on goal that squeaked through Filip Gustavsson with 10:14 remaining in regulation.
The goal, Morrissey's fourth of the season, came on his career-high ninth shot on goal in the game.
"I felt like I was engaged in the game today, got a lot of great passes from guys that put me in spots to shoot," said Morrissey. "I had a game here a few weeks ago where I got a bunch of shots blocked so I tried to be a little bit quicker with that and, like I said, I got a lot of great passes."
But with time winding down on the clock, the Jets weren't able to clear the zone. The puck ended up on the stick of Zaitsev at the right point and his blast beat Brossoit over his right shoulder.
"We got two outs and we didn't take the first one and tried to force the second one, and it came off the stick," said Maurice. "You've got three people wearing white jerseys between the shooter and the goalie, right. There's two guys and a goalie there, and there's nobody else there. We didn't lose coverage on it. It's a shot that got through."
Winnipeg is now tied for third in the North Division with the Montreal Canadiens, who earned an overtime victory on Monday night.
The Jets complete the road trip on Wednesday night in Calgary against the Flames.
"I think there are a lot of things that we can build off of. It's tough to continually say that when we keep losing, but we've got to stick together now more than ever and keep battling and keep fighting," said Morrissey. "We've got to find a way to be even better and stick together for our next one here in Calgary."