Gary Roberts and Michel Ouellet also scored, and Evgeni Malkin and Mark Recchi had two assists apiece for the Penguins, who are 6-0-1 in their last seven and pulled within four points of Atlantic Division-leading New Jersey.
Chris Higgins, Sheldon Souray and Andrei Markov scored for Montreal, which remained in 11th place in the East. Michael Ryder had two assists.
Crosby's goal 4:28 into the game contest was the latest of his highlight-reel scores this season. Crosby took the puck in the neutral zone, stickhandled his way through three Montreal players and and flicked a wrist shot while falling to his left to elude a fourth. The puck got past Montreal goalie David Aebischer for Crosby's 30th goal of the season.
Christensen made it 2-0 in the final minute of the opening period when he got his 15th of the season by converting a poor clearing attempt by Aebischer.
The Canadiens entered the game with the league's second-best power play, but were mired in a 1-for-25 slump. That continued through the first period, when Montreal went 0-for-3 with the extra man.
However, the Canadiens snapped out of it with three power-play goals the rest of the way.
Higgins pulled the Canadiens within one with a wraparound goal - his 19th - 3:33 into the second. While on the power play, Higgins took the rebound of Ryder's shot and went around the net.
Souray's blast from the point tied the score at 2 when it got through traffic and past Penguins goalie Marc-Andre Fleury. It was Souray's 24th goal of the season.
Pittsburgh appeared to put the game away by scoring twice in a 40-second span early in the third. Christensen's second of the game - off a pass from Malkin, who was behind the net - made it 3-2 with 16:20 to play in regulation. Gary Roberts scored his 16th at 4:20, poking a rebound of Colby Armstrong's shot underneath Aebischer.
But the Canadiens responded just 40 seconds later. Given a power play due to a high-sticking penalty on Recchi, Markov tapped in a perfect pass from Saku Koivu into an open net behind Fleury for his fifth goal.
Ouellet restored the Penguins' two-goal advantage at 13:47 when he deftly handled Malkin's pass out of mid-air on a 3-on-2 break.
Crosby added an empty-netter - the first of his career - to give him a league-high 106 points.
Notes: Montreal RW Alexei Kovalev did not play against his former team, missing his second straight game due to vertigo. ... Canadiens C Radek Bonk also did not make the trip to Pittsburgh because of the flu. ... LW Sergei Samsonov, Montreal's third-highest paid player, was a healthy scratch for the third game in a row. ... D Alain Nasreddine assisted on Roberts' goal for his third assist in his past three games. He had one on the season coming into the week.
