Montreal is now 10-2-0 in its last 12 games.
With the game tied 3-3, Gionta was credited with his second goal of the game when his shot, which was initially saved by Gustavsson, bounced off defenceman Brian Lashoff's skate and into the net. Galchenyuk added a fifth for the Canadiens two minutes later.
With the victory, the Canadiens remain in second place in the Atlantic, four points clear of division-rivals Tampa Bay, which lost on Saturday.
With Montreal up 3-0 going into the third, Detroit made a game of it with two goals in 36 seconds to put the Canadiens on their heels. Datsyuk scored his 16th of the year at 5:11 on the power play, and Glendening reduced the deficit again at 5:47 on a soft backhand shot that Price got a piece of.
Kronwall tied it up for Detroit midway through the frame, beating Price with a slap shot from the point on the man advantage.
Despite the loss, the Red Wings are holding on to the first of two wild card spots in the East.
Montreal opened the score when Bournival scored his seventh of the year — and first in 37 games — at 14:16 of the first period.
The rookie got the play going, intercepting the puck in the neutral zone before feeding Ryan White at the blue-line. White held off defenceman Kyle Quincey and took a weak backhand shot on Gustavsson, who kicked the puck straight to a wide-open Bournival.
Pacioretty made it 2-0 on a great individual effort at 8:52 of the second, going around Kronwall with speed at the Canadiens' blue-line to generate a breakaway. Pacioretty fended off a diving Lashoff before beating Gustavsson blocker-side for his ninth goal in his last eight games.
Gionta got in on the action five minutes later, scoring his 16th of the season after a set play off the end boards landed perfectly on his stick, unmarked in front of the net.
The goal was Montreal's second in the period on only their third shot.
Both Montreal and Detroit were coming off wins on Friday. The Red Wings scored three times in the first period to beat the Buffalo Sabres 3-2, while the Canadiens scored seven straight to down the Ottawa Senators 7-4. Both Price and Gustavsson had the night off on Friday.
Notes: The Canadiens play three more times before the start of their first-round playoff series… The game was Gionta's 300th with Montreal… Forwards Brandon Prust (upper body), Travis Moen (concussion) and Dale Weise (upper body) did not dress… Defenceman Douglas Murray served his second of a three-game suspension for his elbow to the head of Tampa Bay's Mike Kostka… The Red Wings are seeking a 23rd consecutive playoff appearance.