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.
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.
