McLeod put Edmonton ahead 1-0 at 1:00 of the first period. He skated around Sharks forward Anthony Duclair in the high slot before scoring glove side from the left circle.
Hyman scored his 20th of the season to make it 2-0 at 10:15. He tapped in a centering pass from Connor McDavid after San Jose turned the puck over in the neutral zone.
"The start really put some momentum in our favor, and it starts the game with a lot of people feeling confident out there on the ice," Nurse said. "Whenever you have a big start, especially coming off a break, it’s easy to wade yourself into the game and not get out to the start that you want."
Bouchard increased the lead to 3-0 at 14:55 with a one-timer from the left point through traffic. Leon Draisaitl then made it 4-0 at 17:32 from in front after Warren Foegele dug the puck out along the boards.
"We gave them too much in the first," Sharks forward Tomas Hertl said. "We're [playing] on a back-to-back, but that's no excuse. This is a team that can score goals, and it seems like every time we have a great two or three chances, we have nothing and then they go the other way and score a goal."