It was almost exactly the way Canada won the gold medal under Babcock at the Olympics in Sochi.
And, it worked again this time as Gustav Nyquist's rebound goal with 28 seconds left in overtime led the Red Wings past the Canadiens 2-1.
"(Babcock) always stressed that we play this way," said Johan Franzen, who returned from a concussion to assist on both of Detroit's goals. "This is how you win games.
"Especially coming down the stretch here and going into the playoffs, this is how you have to play hockey. You've got to track like never before, and always be above their guys and make it small for them so you can create turnovers. Then you give your team a lot of opportunities."
Franzen set up a power-play goal 14:01 into the first period by Todd Bertuzzi for Detroit.
Babcock's defense-first style helped Canada go 6-0 at the Olympics, surrendering only three goals along the way. Gionta's goal was the first against a Babcock-coached team since Lauris Darzins got one at 15:41 of the first period of Canada's 2-1 quarterfinal win over Latvia.
Canada shut out the United States 1-0 in the semifinals and then topped Sweden 3-0 in the final Sunday.
"It's tough to compare," Nyquist said. "It's a different style of game on a smaller rink here. It was an adjustment for a few guys out there, but it was nice to get the win."
There were a handful of Olympians of both sides who had trickled back over the past week as their teams were eliminated.
It made for slow, scrambling hockey with few good scoring chances on either side. Detroit had a 30-20 shot advantage, and fans booed as Montreal tested Jimmy Howard only twice in the second period.
"I'm sure guys noticed the time difference a bit," Nyquist said. "You have to battle through it. It was the middle of the night in Sochi, but we've been back for three days and we're starting to get it back. We'll get some sleep before we play in Ottawa (on Thursday night)."
The Canadiens salvaged a point when Gionta collected a puck at the side of the net in a scramble and backhanded the tying goal into a top corner.
"The execution was not there tonight for both teams," Montreal coach Michel Therrien said. "Both teams played solid defensively. There wasn't much space on the ice, but we put ourselves in position to get a point. It's disappointing that we didn't score in overtime or get to the shootout."
Franzen fed Bertuzzi at the edge of the crease for a power-play goal 14:01 into the game after P.K. Subban was called for roughing.
Bertuzzi returned to the lineup after missing eight games with an upper-body problem. Franzen had sat out six in a row and 21 of the last 22 with his concussion, but said he felt fine after the game.
In overtime, Franzen tipped Danny DeKeyser's shot and the rebound went to Nyquist for a shot into an open side.
Budaj had been slated to start in goal for Montreal even before Canadian Olympian Carey Price suffered a lower-body injury during the team's game-day skate. He is expected to start again when Montreal visits Pittsburgh on Thursday night.
The 21,273 at the Bell Centre gave a rousing ovation to 12 members of Canadian men's and women's hockey gold medal teams in a pregame ceremony. The biggest cheers went to Marie-Philip Poulin, who had two goals in the women's final, and to Babcock and Canadiens players Price and Subban. ... Canadiens Alex Galchenyuk and Travis Moen returned from injuries, but Michael Bournival and Brandon Prust remain sidelined. Goaltender Dustin Tokarski was recalled from AHL Hamilton. ... The Red Wings played the 3,000th road game in their history. They are 1,086-1,439-475 away from Detroit.