Kicker Sean Whyte accounted for nine of the Alouettes points as he booted two field goals, two singles and a convert in the victory.
The win was the fourth in the past five games for the Alouettes (5-8), who are in first place in the East Division following a 1-7 start to the season.
Ottawa (1-11), meanwhile, has now dropped nine straight games. However, the Redblacks did give their fans a rare treat in Friday's loss.
Prior to a touchdown run from running back Jonathan Williams in the final minute of the second quarter, Ottawa hadn't scored a touchdown at home since defensive lineman Jonathan Williams had an interception return for a touchdown in the opening two minutes against the Calgary Stampeders back on Aug. 24th — a touchdown drought of 33 days.
That was all the scoring the Redblacks had as their offence sputtered after scoring a season-high 32 points during a loss on the road to the Saskatchewan Roughriders last Sunday.
"It has nothing to do with being at home, we just have to make it happen," Redblacks quarterback Henry Burris said.
"We had ample opportunities but we didn't convert on third and shorts on multiple occasions. We just have to be better. It's frustrating because it's a game, like how many others, that we could have won."
The only offence in the second half were a pair of punt singles — one for 54 yards and the other 65 in the opening seven minutes of the third quarter — and a 16-yard field goal nine minutes into the fourth from Whyte.
Neither quarterback was particularly effective. Burris completed 25 of 32 passes for 253 yards while Jonathan Crompton was 14 of 29 for 181 yards.
Burris had the Redblacks on the Montreal seven-yard line with two seconds to play, but couldn't handle the snap and was sacked. Ottawa drew a penalty on the play in any case, ending the game.
Montreal was using a prevent defence on the final series that allowed the Redblacks to move the ball from their own 20-yard line. In the end it worked.
"You go into a prevent defence and people always say you're preventing yourself from winning, but they had to score a touchdown and then score a two-point conversion," Montreal coach Tom Higgins explained.
"We did what we needed to do and it might not have been pretty, but it was one of those things that during a course of a season you have to win by hook or by crook. It doesn't matter if the offence does or the defence does it or the special teams."
The Redblacks had more opportunities in the first half of the game, but after 30 minutes it was the Alouettes who were more opportunistic.
Montreal led 10-7 at the half, but that lead was 10-0 until the final minute of the second quarter when Williams scampered 23 yards to score the Redblacks first offensive touchdown at home in just under 16 quarters of football.
Prior to that the Alouettes got a 14-yard field goal from Whyte 10 minutes into the second quarter and a fumble return for a touchdown from Chip Cox at 14:21.
Cox ran the final 50 yards for the TD after Aaron Lavarias recovered the Burris fumble, forced by Bear Woods, and rumbled the initial 25 or so yards before lateralling the ball to his teammate.
"He's a big strong guy and when you have a chance on Burris you have to come down hard and pull those arms and go for the ball," Woods said.
"We're trained to get the ball out and I had a perfect opportunity when Lavarias came in, ran our stunt perfectly and it was a freebie for me. I'm glad he's the one that got the fumble recovery because he's the one that set the whole play up."
Jasper Simmons and Abdul Kanneh each intercepted a Crompton pass in the first quarter that led to good field position.
The interception by Simmons gave the Redblacks the ball on the Montreal 36 but nothing became if it despite a first and goal from the one-yard line.
The second interception gave Ottawa the ball on the Montreal 41, but four plays later Burris put the ball on the ground and Montreal took the lead.
"I was just trying to make a play to help my team win the game," Kanneh said.
"It's very frustrating because we're all competitors and we never want to lose, but it's adversity now. As time goes on we'll get over it and the W's will start piling up. We're playing good football out there and it's just little things that we need to improve on. Once we do the train is going to start moving."
The two clubs combined for just 106 yards of total offence in the first half, with 60 of those yards coming from the Redblacks.