The Jets won their second straight to start a six-game road trip. Winnipeg defeated New Jersey on Monday. The Jets continue their trip at Philadelphia on Friday before playing the Rangers next week.
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.
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.
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.
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.
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.
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.
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.
NOTES: The Islanders continued to be without defencemen Brian Strait (upper body) and Lubomir Visnovsky (concussion). ... The Jets were missing defencemen 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.