Tyler Seguin scored on the power play to tie it 3-3 at 17:56 when he deflected Marchment's shot in the slot.
Warren Foegele put Edmonton ahead 4-3 at 11:46 of the third period after Dallas defenseman Miro Heiskanen turned the puck over in the defensive zone.
"It's five guys out on the ice that make mistakes," Seguin said. "We had a couple of looks there in the third. We had a chance; the game was there. Learn from it, obviously it's a tough situation after the long road trip.
"Every team does that. Every team has those games where they've got excuses if they want them, and we don't want them."
McDavid made it 5-3 at 16:17 with his 29th goal when he put the puck five-hole to finish a 2-on-1 with Hyman. He has 30 points (13 goals, 17 assists) during his streak.
Janmark scored into an empty net at 16:49 for the 6-3 final.
"I think we just played tight, we didn't give them much," Hyman said of the Oilers' play in the third. "I think we just stuck with the game plan and had full contributions. I think we have a really good team, and we're better than our record shows."