Bourque was acquired by Montreal in the 2012 trade that sent Mike Cammalleri to Calgary. Coming into the game, Cammalleri had amassed 72 points with the Flames since the deal -- Bourque had 30 with the Canadiens.
He added a big one against his old team.
"I was getting a lot of quality scoring chances this last week. It's nice to finally get one," Bourque said. "It doesn't really matter who you're playing anymore. I've been gone long enough. But it was nice to contribute."
Bourque scored at 16:15 of the second in his second game against his old team. He was credited with his eighth goal of the season when Brandon Prust's pass banked off his left leg and past Reto Berra.
"Prust just waited for the defenseman (Dennis Wideman) to go down, got around him, and threw it out in front," Bourque said. "It went off my shin pad."
Carey Price made 27 saves in his fourth shutout of the year and second in four games. David Desharnais added an empty-netter for the Canadiens (30-21-6).
Berra stopped 25 shots for Calgary (21-28-7).
"We can't fault Reto for his effort," Flames coach Bob Hartley said. "It gave us a chance to win. He came up with big saves at the right time."
With the game still scoreless early in the second period, Calgary had a chance to take the lead with a full two-minute, two-man advantage.
Tomas Plekanec was in the box for roughing, as well as Lars Eller for handling the puck on the ensuing faceoff, but Calgary's struggling power play took only three shots on Price.
"Not acceptable, obviously," Cammalleri said. "It's crucial for us to get that goal."
Cammalleri was facing his former team for the first since the trade.
"It was a timely 5-on-3," he said. "If we had been a little more patient, we might have gotten the look we were looking for."
Instead, the Flames, ranked 26th in the league with an extra skater, only took shots from the perimeter and had little traffic in front of the net.
Price earned his 22nd career shutout, tying Jose Theodore for seventh on Montreal's career list.
The Canadiens, the league's third-best short-handed team, have killed off 27 straight penalties. They last allowed a goal while playing with a man down on Jan. 24 against Detroit.
Hartley also looked to the Canadiens' big penalty kill as the game changer.
"When you don't score with an opportunity like that, the rule is, in hockey, you just can't get the win," he said. "We could have given the game a different look."
The Canadiens improved to 25-0-3 when they have the lead after two periods.
Dale Weise, 25, made his Canadiens debut playing on the fourth line with Ryan White and Michael Bournival. Weise was traded to Montreal from Vancouver for defenseman Raphael Diaz. ... The Habs cap their four-game homestand against the Vancouver Canucks on Thursday, while the Flames play the New York Islanders. ... Berra got the nod in the net in place of Karri Ramo, who injured his lower back in the first period of Calgary's 4-3 overtime win over Minnesota on Saturday.
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MONTREAL, QC - FEBRUARY 4: Dale Weise #22 of the Montreal Canadiens, who just joined the team, warms-up before...