Bou was the hero for the hosts in the 95th minute when the Designated Player connected on a curling right-footed strike from 25 yards out that eluded a lunging Clement Diop.
New England increased its pressure late in the opening half, repeatedly peppering Diop's goal until Carles Gil broke the deadlock seven minutes before the interval. Bou found the Spaniard with a looping ball into the box, and Gil showed his quality with a first-time volley that eluded Diop at the far post.
Gil's opener was the 13th goal the Impact have conceded over the last 16 games during the 15 minutes before the half, an area of concern Thierry Henry had highlighted prior to the game.
Romell Quioto was Montreal's biggest threat on Friday at Gillette Stadium in Foxborough, Massachusetts, and the Honduran international was rewarded for his bulldozing efforts just after the hour mark. Rudy Camacho leaped to head Amar Sejdic's free-kick toward Quioto, who scored his first playoff goal with a headed effort to level the score.
New England had all the late momentum, and Adam Buksa nearly won the game in the 92nd minute, but Diop palmed his glancing header off the post and away from danger. Minutes later, Diop wasn't as fortunate when Bou's perfectly placed strike found the bottom corner.
Five-time MLS cup champion Bruce Arena has now earned 33 career playoff victories as a coach, surpassing the late Sigi Schmid for the most all time.
Arena's Revs will now face the Philadelphia Union next Tuesday.