Alex Galchenyuk and Max Pacioretty also scored for the Habs (3-3-1), while Price made 29 saves.
Cory Conacher was the lone goal scorer for Ottawa (4-2-0). Craig Anderson stopped 22 shots.
The Senators outshot Montreal 30-25.
This was Montreal's second game in as many against the Senators. Ottawa beat Montreal 5-2 on Wednesday.
The Senators, who have played three games in as many nights, fielded a much younger - and less-experienced - team on Thursday. Veterans Jason Spezza, Chris Neil, and Erik Karlsson were all healthy scratches.
Ottawa got on the scoreboard first when Conacher tapped a loose puck into the net at 5:09 of the first.
Price stopped the initial Chris Wideman shot from the blue line, but neither he nor Andrei Markov could clear the puck. The goal was Conacher's third of the pre-season.
Galchenyuk tied the score late in the first, completing a nice tic-tac-toe play between him, Lars Eller, and Daniel Briere.
Plekanec gave the Canadiens the lead, and the eventual win, at 18:06 of the second period, firing a shot in the roof of the net from the face-off circle to Anderson's right.
Max Pacioretty doubled the Canadiens' lead mid-way through the final frame.
Earlier in the day, the Canadiens announced that eight players had been assigned to the Hamilton Bulldogs, the Habs' AHL affiliate, including forward Christian Thomas and defender Greg Pateryn.
The Canadiens open the regular season at home against the Toronto Maple Leafs on Tuesday, Oct. 1.