Defenceman Andrej Sekera had a pair of assists for the Hurricanes to give him 31 on the season to go with 11 goals.
Jets centre Bryan Little scored his 21st goal of the season for Winnipeg (32-31-9) 1:27 into the third period.
Winnipeg, which heads out on a five-game road trip beginning Monday in Dallas, remains at 73 points. Heading into the game, the Jets were six points back of the final wild-card spot in the Western Conference.
The Jets were coming off a 5-4 overtime win against Colorado on March 19. The loss to Carolina was Winnipeg's 40th one-goal game this season and they are 18-13-9 in those outings.
Carolina, which lost 3-2 to Chicago Friday night, is 2-3-0 in its last five games.
Ward was the difference in a scoreless first period.
Winnipeg had a two-man advantage for 42 seconds early in the first, but Ward opened on a roll and Little was twice the victim.
Ward's quickness helped him get his pad in line to defend a Little shot during the 5-on-3 as the Jets mounted an early 9-0 lead in shots on goal.
Later in the period, it looked like Little was going to score into a wide-open side of the net, but Ward whipped out his stick and the puck hit the paddle.
Winnipeg closed the first period ahead 13-6 in shots on goal.
Slater was a factor in two goals in the second period, in good and bad ways.
His first goal, in his 17th game of the season, began with him winning the face-off back to defenceman Mark Stuart. The blue liner shot the puck and it deflected off Slater past Ward.
But the 1-0 lead barely lasted as Carolina scored the first of three straight goals in two minutes and 53 seconds.
Eric Staal's made it 1-1 and then Jordan Staal made it 2-1 just over a minute and a half later when he went through Jets defenders and scored over Montoya's blocker at 10:10 while Slater was in the penalty box for tripping.
Just 68 seconds after that goal, Nash scored after going around the back of the net with the puck and then banking it off Montoya for the 3-1 lead.
The Jets, who were outshot 21-8 in the second, were working without defenceman Zach Bogosian, who left the game in the period with an upper-body injury.
Winnipeg closed the gap 3-2 in the third when Michael Frolik passed the puck from the back of the net to Little at the front, who made his shot count.
It appeared Stuart tied it up six minutes later, but the goal was waved off for goaltender interference as Jets defenceman Dustin Byfuglien fell on top of Ward in the crease and was lying on his right arm.
Winnipeg pulled Montoya with about 65 seconds left in the game and swarmed Ward, but the veteran held tough. The Jets outshot the Hurricanes 14-5 in the third.
Notes: Jordan Staal's power-play goal was the first the Jets have allowed at home in five consecutive games. Winnipeg's penalty kill was ranked fifth-best (84.8 per cent) in the NHL heading into the game … The game was the second one of Carolina's 18th set of back-to-back games this season. It plays two more. Only Jersey has more back-to-back sets this season with 22. The Hurricanes so far are 9-8-1 in the first game of their sets and 5-10-3 in the second game.