The Senators took advantage of Montreal's backup goaltender to eliminate the Canadiens in five games. Ottawa won the final three contests in the Eastern Conference quarterfinals and outscored Montreal in the series 20-9.
Ottawa became the first team to advance in the East and did so as the No. 7 seed.
Montreal starter Carey Price was unable to play due to a lower body injury and Peter Budaj, who made just 30 appearances over the last two regular seasons, was called on to keep the Canadiens' alive in the playoffs.
Budaj wound up allowing six goals on 29 shots, the key score coming when Kyle Turris tallied shorthanded midway through the second period to give the Senators a 3-1 lead.
Conacher scored with 7:34 to go in the first to give Ottawa a 2-0 advantage and he tacked on one of the Senators' three third-period goals.
All three of the goals in the final period came on the power play as Montreal sent a parade of players to the penalty box.
Three roughing penalties another for high sticking were called in the third period and the game finally deteriorated in the closing minutes, leading to gross misconduct penalties to Conacher and Montreal's Gabriel Dumont and Michael Bluden.