Chiasson scored for the second game in a row, tallying his sixth of the year as the Oilers won their third straight and extended their point streak to five games.
The Orange & Blue also improved to 24-17-5 on the season and 3-0-1 on their current five-game road trip.
"I was a Habs fan," Chiasson started post-game, "my mom and dad used to bring my sister and I to the game here and it's always special coming to this building.
"I'll remember this one for a long time."
The winger's performance in Montreal marked the second straight game a local product was able to contribute in a big way after Captain Connor McDavid was the hero in his Toronto homecoming.
"I guess we have to go to Sweden," joked Oscar Klefbom, who made the heads-up play to find Chiasson's blade in the slot for the redirection.
The Oilers didn't get the start they were looking for but battled back when Last Man In candidate Ryan Nugent-Hopkins hit the double-digit goal total with his 10th at 2:16 of the third to capture the equalizer.
The NHL All-Star hopeful finished the night with two points, adding an assist on Josh Archibald's empty-net goal late.
"The third period, we got our feet moving a little bit and were able to capitalize on a couple," Oilers Head Coach Dave Tippett said.
"I felt that power-play goal really did that for us."
Edmonton began the 2nd trailing 1-0 and were quickly dealt a two-goal disadvantage when Jesperi Kotkaniemi walked in and sniped top corner from the slot less than three minutes into the middle period.
"They were a desperate team, they were a quicker team, they were on loose pucks, they were executing and we weren't," Tippett said of the Canadiens' play during the first two periods.
Riley Sheahan replied by showing off some fine target practice of his own. Joakim Nygard got tangled into a board battle along the half wall in the Habs' zone and exited with the puck in his possession. He poked it over to Sheahan who didn't allow netminder Carey Price any time to get set, putting it upstairs for his fifth of the year.
"They were a good line for us," Tippett said of Sheahan, Nygard and Archibald. "They played really hard and gave us a boost."
Mike Smith, appearing in his fourth consecutive match for the Oilers, played his part in the second with some timely saves to keep the game from getting away.
The keeper denied Montreal's first goal scorer Philip Danault on the doorstep then got some help from the post when Nate Thompson attacked on a breakaway, beating Smith on his backhand but not the iron. Smith ended the night steering aside 35 pucks and altered his record to 10-9-3.
"He's added really good leadership to our group here," Tippett said. "If he had some things to say (during the second intermission) I'm sure they were words of wisdom."
Edmonton will travel to Calgary for the second Battle of Alberta of the season on Saturday.
"The one thing we're trying to key on here as players is to try to keep building our game," Chiasson said.
"You got to figure out a way to get points. That's what good teams do."