Dube tied it 2-2 at 8:16 of the third period with a shot from the left hash marks off a cross-ice saucer pass from Tyler Toffoli.
Huberdeau put Calgary in front 3-2 at 9:33 when his no-look pass from the top of the crease deflected in off the skate of Derek Forbort.
"We stuck with it," Huberdeau said. "I think we were playing well. We deserved to come back in this game, which we did. We just have to (stick with it). I think it's happened too many times this year (trailing in the third period). That's the kind of stuff we need to figure out."
Pavel Zacha tied it 3-3 at 14:07 when he tapped in a backdoor pass from Orlov on a power play.
"In games likes these especially, there's a lot of emotion, fatigue," McAvoy said. "You're up 2-1 and it's emotional. You know you're not playing well and kind of hanging on a little bit. Then it's 2-2, then it's 3-2, and we still find a way to come back like we have all year. You can take a lot of confidence from games like those."