Little scored a tiebreaking goal late in the third period, Montoya made 28 saves, and the Jets beat the Lightning 2-1 on Thursday night.
"We knew it was going to be a tough road game," Montoya said. "We knew we had to keep the score down, and that's what we did."
Little slid the puck from in-close past goalie Anders Lindback with 4:08 to play. Winnipeg also got a goal from Eric Tangradi.
"I had a bit of room and it opened up," Little said. "I wasn't really aiming anywhere. I just tried to sneak it through."
The Jets were beaten by the Lightning 8-3 on Feb. 1. This outcome was much different.
Montoya made a couple of strong saves, including on a left-circle shot by Steven Stamkos, during a 2-minute, 5-on-3 Tampa Bay power play midway through the second period. The Lightning's two-man advantage came after Paul Postma (interference) and Mark Stuart (high-sticking) were both given minor penalties at 7:57.
"He's great in the room ... he's great on the ice," Jets defenssman Zach Bogosian said of the backup goalie. "It's good to see him go in there and battle, and he works hard, and he shows it in his game."
Stamkos got his 18th goal this season for the Lightning, who have lost six of seven.
"It's not fun when you're losing," Stamkos said. "Obviously, you've got to produce, but you want to do it when the team is winning. Feels a lot better that way. When you're not winning, then maybe there's more I can do, we can do as a team."
Stamkos tied it at 1 when he skated into the low slot and put a shot past Montoya after taking a pass from Martin St. Louis 6:57 into the third period. St. Louis has five assists and seven points during a five-game points streak.
"I thought in the third period we were the better team, but they got a chance and they score, and we hit the post and their goalie makes some big saves," Stamkos said.
Tangradi stopped a personal 49-game goal drought dating back to Oct. 15, 2010 against the New York Islanders and put the Jets up 1-0. The centre beat Lindback from the low left circle midway through the first period.
Winnipeg, which entered with the NHL's lowest-ranked short-handed unit, killed off all five Lightning power plays.
"Awesome job," Montoya said. "They had a tough time entering the zone, and when they did, and when there were loose pucks in the zone, we were pouncing all over it. I had to make one or two saves, but I knew where the puck was going, so when it did get there, I was there."
The Jets also failed to score during a 50-second, 5-on-3 late in the second period.
NOTES: Tangradi's goal was also his first point in 16 games. His previous point came on an assist against the New York Rangers on April 5, 2012. ... Tampa Bay LW Ryan Malone returned after missing 13 consecutive games with an undisclosed lower body injury and had an assist. ... Thursday was just the fourth time this season the Jets have had the lead after the first period. ... Winnipeg LW Evander Kane had nine of the Jets' 28 shots. ... Stamkos had seven shots. ... Tampa Bay captain Vincent Lecavalier has not scored a goal in the last nine games.