Patrice Bernier and Marco Di Vaio both scored twice for Montreal in their triumph on Sunday, while Diego Fagundez and Kelyn Rowe struck for the Revolution.
The Impact maintained top spot in Major League Soccer's (MLS) Eastern Conference with their win over New England but it could have been a lot different if referee Sorin Stoica had kept his red card in his pocket in the fifth minute.
New England could have moved into fourth in the Eastern Conference if they had overcome Montreal, after Philadelphia Union lost 1-0 away to San Jose Earthquakes, but the Revolution's chances of victory suffered a fatal blow when Reis brought down Di Vaio early on at Gillette Stadium.
Montreal midfielder Felipe Martins curled a cross over New England's defence to Di Vaio and although the Italian striker missed his shot, he was tripped by Reis as he attempted to chase down the loose ball.
Despite doubts over whether Di Vaio would have retrieved the ball before it rolled out of play, Stoica decided Reis had denied a clear goal-scoring opportunity, which meant not only a penalty but a red card for New England's goalkeeper.
After a tirade of denial from Reis and his Revolution teammates, Bernier eventually stepped up to the spot and scored past New England's substitute goalkeeper Bobby Shuttleworth.
Despite playing with 10 men, the home side equalised in the 26th minute through Fagundez but trailed at half-time after Montreal were granted another penalty when New England defender Jose Goncalves was judged to have knocked over Martins.
Bernier again made no mistake and in first-half stoppage time Di Vaio cut inside Anthony Soares and slotted the ball home to make it 3-1.
Di Vaio completed his brace in the 56th minute when he brought a long ball down and fired his shot into the bottom corner of Shuttleworth's net and although Rowe curled in a fine solo effort in the 76th minute, Montreal held on for victory.
The win took Montreal to 45 points, ahead of New York Red Bulls and Sporting Kansas City due to having played fewer games.
The Red Bulls thumped Houston Dynamo 4-1 on Sunday, while Sporting cruised to a 3-0 win over Columbus Crew on Saturday.
Real Salt Lake lead the Western Conference on 48 points despite not playing over the weekend, while Seattle Sounders are second, two points further back, following a 2-1 triumph over Chicago Fire.
In other results, FC Dallas defeated Vancouver Whitecaps 3-1, Colorado Rapids won 1-0 away to Los Angeles Galaxy, Portland Timbers crushed Toronto FC 4-0 and Chivas USA edged out DC United 1-0.
