McDavid scored his sixth goal of the season on another power play to make it 5-1 at 10:58.
"[McDavid] is obviously a really special player and when you have a chance to play with him, you're pretty fortunate because he creates so much space and time and he's able to do a lot of things that nobody else can do," said Hyman, who moved up to McDavid's No. 1 line.
Warren Foegele scored his first goal with the Oilers on a rush following a Clayton Keller turnover as Edmonton took a 1-0 lead at 18:02 of the first. Hyman's shorthanded goal made it 2-0 at 6:31 of the second.
"It's early, there's lots to work on, but I like some of the things we're doing," Tippett said. "Our special teams have been pretty good, we've gotten contributions throughout the lineup a little more than last year. We're off to a decent start, but we've got a lot of work to do yet."
Mayo, a defenseman for making his NHL debut after five seasons with Tucson (American Hockey League), scored at 1:25 of the third to make it 3-1 ahead of Edmonton's two power-play goals.
"I wasn't expecting that, my goal was to play a shutdown game and show I can compete and play up here, and I think I did a good job with that," Mayo said. "I had a lot of energy all day and I was pretty nervous, and I just wanted to go out there and get my legs under me."