McDavid won it for the Oilers with a wrist shot from the slot after a pass from Oscar Klefbom, who carried the puck in from the Coyotes blue line.
"He picks up a pass at his feet on the outside of his skate, which makes it even more impressive," Oilers forward Milan Lucic said. "Playing soccer before the game, his soccer game isn't very impressive, but on the ice his footwork is good."
McDavid scored his 35th goal of the season and first shorthanded at 3:38 of the first on a breakaway created by Alex Chiasson's pass, putting a shot under the crossbar while Coyotes defenseman Oliver Ekman-Larsson tried poking the puck off his stick.
"I thought their [top] line was the difference," Ekman-Larsson said. "McDavid's probably the best player in the League right now. I thought they had an unbelievable game."
Galchenyuk tied it 1-1 with a power-play goal at 18:24 of the first, a wrist shot from the right circle. Conor Garland screened Oilers goalie Mikko Koskinen, who made 28 saves.
"When Alex shoots the puck, he's dangerous," Tocchet said. "He was more aggressive with the puck tonight and he's got to do that."