It was a second straight victory to start a six-game road trip for Winnipeg following a win at New Jersey on Monday.
The Jets continue their trip at Philadelphia on Friday before playing the Rangers, Florida and Tampa Bay next week. They had lost three straight at home -- two in shootouts -- before starting the trip.
"We gave them some life late, but we managed the game well when it counted most," Jets coach Claude Noel said. "Al made some big stops for us and we found a way to hold on."
Stuart's first goal of the season on a blast from the left point right off a faceoff eluded Kevin Poulin to the glove side at 11:27.
Ladd, the Jets captain, made it 2-0 off a scramble in front at 14:39 with his seventh of the season. Setoguchi made it 3-0 with his sixth goal at 16:42.
Defenseman Andrew MacDonald scored for the Islanders at 17:49 of the second on the power play when he took a cross-ice pass from Thomas Vanek at the left point and fired the puck past Montoya.
John Tavares made it a one-goal game at 14:01 of the third when he poked a rebound past Montoya for his team-leading 11th goal of the season. Tavares, who assisted on MacDonald's goal, leads the Islanders with 29 points.
"We need everyone to have the same mindset, play hard every shift and do all the little extra things on the ice," Tavares said. "When we don't do that as a team, we are pretty easy to play against. No question this is frustrating and we need to address it."
Winnipeg's Jacob Trouba went off for hooking at 14:54 of the third, but the Islanders put minimal pressure on Montoya.
The Islanders were coming off a poor road trip, losing at Toronto, Pittsburgh and Philadelphia. They were hoping the start of a four-game homestand would be a turnaround.
But the Jets handed the Islanders their ninth loss in 11 games. New York is 8-14-3 overall, last in the Metropolitan Division.
And since acquiring the high-scoring Vanek in a trade with Buffalo for popular left wing Matt Moulson on Oct. 27, the Islanders are 4-10.
"We have character guys in our room and I know if they keep working, we will turn this around," Islanders coach Jack Capuano said. "When you don't get results, it's tough mentally. You just have to find a way out of it."
The teams played a spirited scoreless first period, featuring end-to-end action at both ends of the rink. The Islanders outshot the Jets 13-11, but failed to capitalize on two power plays.
Both goaltenders played well early. Poulin stopped Matt Halischuk with a flailing stop midway through the second to keep the game scoreless, but the Jets solved the Islanders goaltender shortly thereafter.
The 23-year-old Poulin has struggled since becoming the team's No. 1 goaltender after starter Evgeni Nabokov sustained a groin injury against Detroit on Nov. 16. Poulin has lost four straight starts and has allowed 21 goals in his past six appearances.
"We gave them too many opportunities," Poulin said.
Montoya, the sixth overall pick by the Rangers in the 2004 draft, improved to 3-2-1 as he gave starter Ondrej Pavelec a rest. Montoya never played for the Rangers but did play for the Islanders for two years before joining the Jets last season.
"It felt really good," Montoya said. "It was especially great to win here against the organization that gave me a chance in the NHL."
The Jets are playing their first season in the Western Conference after the past two seasons in the east. They moved to Winnipeg from Atlanta after 2010-11, but the league didn't move them until realignment was implemented before this season.
The Islanders continued to be without defensemen Brian Strait (upper body) and Lubomir Visnovsky (concussion). ... The Jets were missing defensemen Zach Bogosian (groin) and Paul Postma (blood clot) and forward Jim Slater (sports hernia). ... The Islanders are 0-12-1 when they score fewer than three goals. ... The teams also meet March 4 in Winnipeg.
Copyright by STATS LLC and The Associated Press
UNIONDALE, NY - NOVEMBER 27: James Wright #17 of the Winnipeg Jets falls to the ice as teammate Chris Thorburn #22...