Philadelphia, which defeated the Detroit Red Wings 6-1 on Friday, had 22 points (9-4-2) in November, the most by an Eastern Conference team.
Tomas Tatar scored two goals for Montreal (11-9-6), which is winless in its past seven (0-4-3). Kinkaid made 24 saves.
"I think the boys deserved better," Kinkaid said. "I've got to have that one in overtime. I kind of cheated a little short side, I thought he'd go up top. And the boys played great defensively in front of me, and we were buzzing, Elliott made some huge saves."
Tatar tied it at 3-3 with his second goal of the game on a power play at 3:16 of the third period. He took a cross-ice pass from Nick Suzuki and scored on a wrist shot from the left side.
"I think we showed character in 60 minutes," Tatar said. "We were pretty happy with our game, how it went. It hurts that it didn't go in our way in overtime."
The Canadiens play the second of back-to-back games at the Boston Bruins on Sunday.
Joel Armia gave Montreal a 1-0 lead 19 seconds into the first period on a shot from the right side.