Adams also ran for a pair of TDs to lead Montreal (2-2), while completing 23-of-30 passes.
Dominique Davis was 23-of-37 passing for 268 yards for the Redblacks (2-2) and scored on a four-yard run with less than five minutes to play, but it wasn’t enough.
Already up by 10, Adams scored on a 12-yard run early in the fourth quarter to give the Alouettes a 29-12 lead.
After Ottawa turned the ball over on downs on their own one-yard line Montreal got a one-yard touchdown run from Adams for the final score.
The Alouettes scored the game’s first nine points, with six of those coming off turnovers, before the Redblacks mounted a comeback late in the first half.
Davis had his first pass of the day picked off by Tommie Campbell, who returned the ball to the Ottawa 16-yard line.
The Alouettes were unable to get a first down, however, but a 16-yard field goal by Boris Bede at 2:40 gave the Als an early 3-0 lead.
Bede booted a second field goal before the end of the first quarter, this time from 26 yards at the end of a 62-yard drive, to put Montreal up 6-0 at 12:21.
In the second, following a 16-yard reception, RJ Harris fumbled right into the hands of Campbell who then rumbled five yards to the Ottawa 43. That led to a 34 yard-yard field goal from Bede and a 9-0 lead midway through the second quarter.
The Redblacks were finally able to put some offence together later in the half and a 58-yard drive was completed with a 25-yard Lewis Ward field goal with just over three minutes to play in the half.
After a two-and-out by the Alouettes, Davis once again drove the ball down field completing passes of 42 and 18 yards to Harris, setting up a one-yard touchdown run by the quarterback with 49 seconds left in the half.
Following a penalty to the Alouettes the Redblacks went for a two-point conversion from the Montreal one-yard line, but two offensive penalties on the play pushed the ball back to the Montreal 21-yard line. The Redblacks were forced to attempt another two-point conversion, which was unsuccessful and the teams went into the break tied 9-9.
Ward gave the Redblacks their first lead of the game at 3:35 of the third quarter with a 50-yard field goal, but the next play saw Adams connect with a wide-open Quan Bray for a 75-yard catch and run touchdown, and just 16 seconds after the Redblacks took the lead, the Alouettes jumped back in front 15-12 after a failed conversion attempt.
Late in the quarter Jake Wieneke caught a five-yard TD pass from Adams and the conversion gave the Alouettes a 22-12 lead they took into the fourth quarter.