The Roughriders had a chance to win it on the final play of the game but Tyler Crapigna's field-goal attempt from the 45 was wide to the right.
Boris Bede's fourth-quarter field goal stood up as the game-winning points for Montreal. Durant played his first game since he was acquired in January after 11 seasons in Saskatchewan.
Kevin Glenn, back with the Roughriders after starting last season with Montreal, threw a TD pass to Bakari Grant. Crapigna added three field goals.
Durant marched the ball to the Saskatchewan 37 on the opening drive, but Bede missed the 45-yard field-goal attempt.
Neither side was able to mount much on attack until 10:25 of the second quarter, when Cunningham got behind safety Mike Edem for a 65-yard touchdown reception.
Glenn hit right back with a 10-play drive capped by a 19-yard TD pass to Grant at 13:27, a play that stood up to video review when Grant was stripped of the ball just past the goal line.
A shanked Bede punt gave the Roughriders another chance and, aided by a 33-yard strike to Nic Demski, Crapigna was good from 35 yards for a 10-7 halftime lead.
A 27-yard run up the middle by Cameron Marshall on the opening play from scrimmage in the second half helped set up Crapigna's 40-yard field goal at 3:27.
Montreal answered with an eight-play drive that saw Jackson make a 12-yard TD catch in the end zone at 7:07.
The end of the third and start of the fourth quarter saw three straight possessions end with turnovers _ a fumble by Marshall, a Jonathon Mincy interception and a Nik Lewis fumble. None produced points.
An 18-yard Crapigna boot at 8:04 put the Riders ahead, only to have Bede match it with an 18-yard kick at 12:31.
Alouettes defensive back Travis Hawkins was injured on the first play of the second half and did not return.