Daniel Carr and Sven Andrighetto had goals for Montreal, and Mike Condon finished with 26 saves. The Canadiens, currently the runaway leaders in the Eastern Conference, won all three meetings last season.
Skinner deflected Brett Pesce's shot into the net for a power-play goal with 7:32 remaining to break the 2-2 tie.
Nordstrom had tied it with 6:45 left in the second as he knocked in the rebound of Andrej Nestrasil's shot past Condon stick side.
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