But the Oilers fought right back with a goal by centerman Riley Sheahan just under five minutes later.
Sheahan blasted a wrist shot by goaltender Carey Price to cut the Canadiens' lead to 2-1.
Julien's squad got into penalty trouble early in the third period and ultimately paid the price for it.
With Danault in the box for holding, Ryan Nugent-Hopkins lit the lamp for Edmonton at the 2:16 mark of the frame to even things up.
Then, Alex Chiasson gave the Oilers their first lead of the game when he re-directed an Oscar Klefbom pass beyond Price at the 9:40 mark of the period.
Josh Archibald added an empty-netter for Edmonton.
That's the way things finished up.
The Canadiens will be back in action on Saturday night against the Senators in Ottawa.