Carey Price made 25 saves for his fifth shutout of the season and 30th of his career. With the game still scoreless, 18 seconds before Plekanec scored, Price stopped Red Wings forward Gustav Nyquist from the bottom of the right circle with 2:48 left.
"These are the types of games you want to be good playing in because these are the type of games you'll be playing in the spring (playoffs)," Price said.
He has three shutouts in his past eight games and has allowed two goals or fewer in 11 of his past 12 starts.
"Our team really has confidence playing those games," Montreal coach Michel Therrien said. "We know that if we stick to our plan, good things are going to happen."
"Jumped off the bench. … I saw it was wide open in the middle of the ice and just tried to put myself in the best position to put it in the net," Plekanec said.
The Canadiens (37-15-4) have won five of their past six.
Max Pacioretty added an empty-net goal in the final minute for Montreal, his 26th of the season.
Howard made 27 saves for Detroit (31-14-10) which has lost three in a row.
"It's a tough one, but a great game to be a part of," Howard said. "It definitely felt like a playoff game; no room, tough to get to both nets. It was a lot of fun."
The Canadiens aided Price by blocked plenty of shots.
"I always tell the players to make sure they're in the shooting lanes, make sure they protect the house and keep teams playing on the outside," Therrien said.
It was Montreal's fifth consecutive win over Detroit and third straight this season.
"It was a lot of fun," Nyquist. "Two good teams playing against each other. We played a much better game (tonight) than we did the first two games. Fun game to play. Not so much fun to lose."
Each team had a good scoring chance in the first period, in which Montreal out-shot Detroit 7-6.
Howard knocked away Montreal defenseman P.K. Subban's one-time slap shot from the high slot with a little over eight minutes left.
Price made a glove save on forward Darren Helm, who had a breakaway from the high slot area after a give and go play with Nyquist off the rush, with 3:07 remaining.
Price stopped Henrik Zetterberg's tip attempt with a toe save late in the second period.
Detroit defenseman Brendan Smith covered up his own miscue 9:25 into the middle period when he was able to knock the puck away from Brandon Prust on a breakaway chance after Smith gave the puck away to Prust when the Canadiens forward intercepted his pass outside the Red Wings blue line.
The puck almost went in off Howard's back when Montreal defenseman Alexei Emelin's shot bounced off the glass behind the Detroit net a little less than three minutes into the second.
Pacioretty thwarted Luke Glendening's shorthanded breakaway in the final 15 seconds on the second period without taking a penalty.
"It was a check-fest," Red Wings coach Mike Babcock said. "Not much happened. Not much room for either team, not many quality chances. There was good intensity and the next shot was going to win it. It’s a good experience for our guys."