The Canadiens, who won 2-1 in overtime at the Detroit Red Wings on Saturday to begin a five-game road trip, lead the NHL with 34 points.
"Both teams got a lot of quality scoring chances, and both goalies played really well," Montreal coach Michel Therrien said. "I really liked the way we got out of the gate tonight. I thought we were ready to play, we tried to dictate the game. I didn't like the way that we played in the second. They put pressure on us and we didn't react the right way, but we gave it all we got in the third."
Rakell gave the Ducks a 1-0 lead with his ninth goal on a power play at 16:50 of the first period.
Fowler made it 2-0 at 11:56 of the second period. Ryan Kesler assisted on both Anaheim goals.
It was the first time Price has trailed by two goals this season.
"Our start wasn't very good," Fowler said. "Before we were five minutes into the game, they had [eight] shots and we had nothing. They had their legs and were ready from the start. It might've caught us off guard a bit, but we started to get into it. We stayed in the game with some big saves from [Gibson]."