Keaton Ellerby, Jacob Trouba and Anthony Peluso were the other goal scorers as Montoya picked up his second shutout of the season and the Jets won their third straight game, matching their season-high.
Montoya, making his second straight start for the Jets after coming on in relief of regular starter Ondrej Pavelec in the first period of a game last week against Minnesota, won his sixth consecutive decision and upped his record to 8-2-1.
Sabres backup Jhonas Enroth got his 12th start of the season, and handed the Jets (19-18-5) the lead when a weak point shot from Ellerby snuck past his blocker in the first period.
The Sabres (11-25-4) thought they had tied the game when Marcus Foligno banged the puck past Montoya, but the referees ruled the net was dislodged before the puck went in. Video review was inconclusive, so the call on the ice stood.
Trouba, the rookie defenceman, one-timed a Chris Thorburn pass to beat Enroth at 13:06 of the second period for his third goal of the season.
Peluso added an empty-net goal with 1:28 remaining.
Enroth finished with 23 saves on 25 shots.
Buffalo failed to score on four power plays, while the Jets were blanked all three times they had the man advantage.
While Montoya's US$601,000 salary is $3.3 million less than Pavelec's, his play could soon force Jets coach Claude Noel to re-evaluate the way he splits his goalies' workloads.
Pavelec is 11-16-4, with a .902 save percentage, while Montoya increased his save percentage to .934.
The Sabres, owners of the NHL's worst record, had earned points in seven of their previous nine games, including a win against the Jets.
That wasn't Winnipeg's only loss against teams near the bottom of the standings. The Jets had been facing criticism for losses to Edmonton, Calgary and Florida, and vowed before the game that they wouldn't be taking their opponent lightly.
Notes: Buffalo forward Ville Leino, who was shaken up against Washington on Sunday, was in the Sabres lineup but left after just three first-period shifts with a lower-body injury. … Jets forward Thorburn played in his 500th career game. … Winnipeg forward Blake Wheeler's 10 goals in December were second only to Chicago's Patrick Sharp, who had 12.