Montoya, making his fourth start of the season as Ondrej Pavelec got the night off, stopped 28 shots for his third win.
"I thought we played a strong game," Winnipeg coach Claude Noel said. "I thought our goalie was strong in the net for a guy that hasn't played since Feb 10. I thought he was real strong and made some key saves for us.
"That's a really tough task, to come in every 10 games or whatever it is and do the job that he did and be out for that amount of time, it's a really tough task, so our hat goes off to him and I certainly think his teammates appreciate the job that he did."
Montoya agreed that playing sporadically is difficult.
"It's not easy when you go in there every couple of weeks," he said, "but I'm not going to make any excuses. Just be prepared."
Tampa Bay tied the game with 6:57 gone in the third period when Steven Stamkos, unchecked in the slot, one-timed a pass from Martin St. Louis. Ryan Malone, making his return after missing 13 games with a lower-body injury, had the other assist. For Stamkos it was his NHL-leading 18th goal and his 39th point in 26 games against the Jets' franchise.
Although the Jets entered the game with the worst penalty-killing percentage in the NHL (.735), they were able to shut down the Lightning power play.
Tampa Bay had a full two minutes of 5-on-3 time in the second period when Paul Postma and Mark Stuart were called for minor penalties at 7:57. But the Lightning came up empty, managing four shots. Vincent Lecavalier had the best chance but was robbed by a diving stop by Montoya, going across the crease to his left.
"The goalie stopped five one-timers," Lightning coach Guy Boucher said. "At least one of them normally would go in. I certainly wouldn't tell (Stamkos) that he didn't shoot right. Vinny's one-timer, and he got it again and the goalie got it with his glove. The goalie stopped them. The goalie played great."
Tampa Bay was 0-for-5 on the power play.
"For us the turning point of the game was the 5-on-3 penalty kill," Noel said. "It was a full two minutes and it's really hard to see if you can get out of that. It was a key kill. Guys made sacrifices."
The teams were firing with abandon in the first period, combining for 25 shots on net. Winnipeg's Evander Kane, who finished the game with nine shots, had six in the opening period.
The Jets (11-11-1) opened the scoring at 10:05 of the first period when Kyle Wellwood did some hard work keeping control of the puck along the boards while holding off two defenders. He finally found Eric Tangradi, who beat Lindback from a sharp angle from below the faceoff circle for his first goal of the season.
"There wasn't really anywhere else to shoot," Tangradi said. "With the slump that I've been in I was just trying to get as many pucks to the net as I can. I was able to find a little spot and fortunately it went in."
The spot Tangradi found was on Lindback's short side, an area where he has been victimized fairly often and one that has drawn the notice of Boucher.
"I'll let you be the judge," Boucher said tersely when asked if Lindback's short-side goals were a concern.
The Lightning (10-13-1) did not lack for scoring chances, particularly late in the first period when Montoya robbed Tom Pyatt by moving to his left after Pyatt appeared to have an open net.
"This was very difficult for the players," Boucher said. "You get all these chances but they are not going in. I can't go in the room and start blaming the players and blaming the way that they played. It's hard to take. It's hard to take because the results are not coming with the effort. Our players did everything they could tonight but it didn't turn our way."
Stamkos echoed the frustration in the Lightning locker room.
"Yeah, it doesn't matter, one goal, two goals, three goals, a loss is a loss," Stamkos said. "If you don't get a point, it's a loss. We keep saying we are playing well, but if we are not winning then we've got to find a way."
Lindback faced 28 shots and his record fell to 8-6-1.
The loss was the first time in the past 11 games the Lightning failed to gain a point against the Jets' franchise; they had gone 9-0-1 against them.
Winnipeg continues its four-game road trip with a return visit to the Florida Panthers in Sunrise on Friday night. They dropped a 4-1 decision to the Panthers on Tuesday.
The Lightning, and Boucher, will be hoping to find some answers against the visiting Montreal Canadiens on Saturday.
"I'm surprised by the lack of result with the games that we've played that we deserved," Boucher said. "That's tough. When you don't deserve them, it's plain and simple. But when you play like we did today and you don't get anything, those hurt."