It was also their last game at Canad Inns Stadium.
Both teams played backup quarterbacks, Montreal because they chose to sit Anthony Calvillo and Winnipeg because Buck Pierce was hurt for the third time this season.
The result leaves the Bombers at 6-12, tied on points with Hamilton but ahead thanks to the series edge, leaving the Tiger-Cats in last place in the CFL. The win cost the Bombers first pick in the 2013 CFL draft but coach Tim Burke wasn't complaining.
"It feels really good to get a win, obviously, and I think it's a good positive step for next year," he said.
He had good things to say about both quarterbacks but singled out Justin Goltz, who came in for the fourth quarter and scored the go-ahead touchdown.
"You could see his athletic ability. He can run, he can throw, he's a big guy, I think he's got a really good future. . .
"I think there were some real positives in his performance and enough to say to yourself 'boy, we really want him back'."
With Pierce missing 11 games this season and failing to finish others because of injury, the Bombers are taking a hard look at what to do with the quarterback position for 2013.
The Alouettes still finish first in the CFL East Division at 11-7 but quarterback Adrian McPherson failed to capitalize on the 10-0 first quarter lead he built in his first start this season.
"I'm really disappointed we didn't get the win," he said.
"I didn't feel too bad, especially for someone who hasn't played in so long. . . I'll go back watch the film and see how I can try and get better."
Winnipeg cornerback Jovon Johnson, who set up Goltz's touchdown with a 71-yard punt return, said the win was important for a team that has struggled.
"We talked about it before the game. . . Our season for next year starts today," he said.
"Right now it just means were headed into the right direction, going out with a win, hopefully we can carry over some momentum from that and bring it back for next year."
Goltz replaced Alex Brink in the fourth quarter after Brink completed 17-of-26 pass attempts for 173 yards and one interception.
McPherson scored one touchdown and was also his team's leading rusher with 102 yards.
Brink and McPherson both handle wildcat plays for their teams and Brink was second on the Bomber rushing list at 58 yards.
"I think I played well tonight. We executed, we moved the football, we had only one or two and outs," Brink said.
"For the team to go out on a high note going into the off-season, obviously with the stadium closing, to send it out with a victory is huge."
Burke wasn't happy that his team got off to another slow start, although this time they managed to find their feet and stage a comeback.
Sean Whyte kicked a 17-yard field goal to put Montreal on the board at 4:10 of the first quarter on the Alouettes opening drive. McPherson's touchdown made it 10-0 about six minutes later.
Justin Palardy's 24-yard field goal a few seconds into the second quarter got Winnipeg on the board and the Bombers picked up two singles on a missed field goal and a punt to trail 10-5 at the half.
The second half was all Winnipeg as Montreal managed only a single and Winnipeg got another field goal, Goltz's touchdown and a single.
The Bombers lost their best receiver in the third quarter when rookie Chris Matthews was crushed to the turf by Montreal's Kryies Hebert.
He was out cold and took a few minutes to regain his feet but said after the game he felt fine. He also added another 55 yards to his total for the season, brining him to 1,192, good enough for sixth in the CFL.
An announced crowd of 26,807 fans got a second chance to say goodbye to Canad Inns Stadium Saturday but it looked like a few ticket holders may have decided to stay home on an overcast day with temperatures hovering just above freezing.
The stadium, known simply as Winnipeg Stadium for most of its existence, is just a year shy of its 60th birthday.
It was feted last year, when the Bombers thought they would be playing this season at Investors Group Field, located at the University of Manitoba.
Construction delays have plagued the project, which has yet to be finished.
This was also the Canadian Football Hall of Fame game honouring this year's inductees.
The players are quarterback Damon Allen, who played with four CFL teams winning three Grey Cups, 14-season all-star Bombers' receiver Milt Stegall, Saskatchewan offensive lineman and kicker Jack Abendschan, Montreal running back Eric Lapointe and the late linebacker Tyrone Jones, who also played in Winnipeg.
The builders are B.C. Lions and Toronto Argonauts owner David Braley and former University of Calgary coach Peter Connellan.