Danault was taken off the ice on a stretcher after he was hit in the head by a slap shot from Bruins defenseman Zdeno Chara.
Price made 29 saves through overtime for Montreal, which has won just twice in eight games.
Galchenyuk took a diagonal feed from Jonathan Drouin in the right circle and beat Rask with a wrist shot under the crossbar on a power play at 8:51.More news: BBC pundit has transfer advice for Newcastle United
He was moving and appeared to be speaking to medical staff before he left the ice, to an ovation from the Bell Centre crowd.
Boston countered on the power play at 17:40, with Patrice Bergeron taking the puck along the boards and feeding it to Marchand in front of Montreal goalie Carey Price. Danault was carried off the ice on the gurney and taken by ambulance to hospital for observation. Deslauriers picked up a loose puck at the Boston blue line and beat Tuukka Rask with a low shot from the slot at 5:45.
The Canadiens issued a statement during the third period that said: "Danault suffered a head injury".More news: Brightline's 'higher speed' train service will begin this weekend in Florida
"There's no doubt it's a special thing because I spent a lot of great years in (Boston) with an organization that treated me extremely well and I'm showing a lot of gratitude towards them for that", Julien said before the game Saturday.
All even after one: Max Pacioretty gave the Canadiens a 1-0 lead when he scored at 3:22 of the first period on the rebound of a shot from the blueline by rookie defenceman Victor Mete, who was making his first appearance since helping Canada win the gold medal at the world junior championships. It happens. It's unfortunate. "He is awake and moving". Hopefully Phillip is now recovering. "I'm obviously wishing him a fast and full recovery". "So I was glad that he was doing OK".More news: Accenture (ACN) PT Raised to $152.00 at Barclays
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