Erik Haula gave New Jersey a 1-0 lead at 4:45 of the first period on a wrist shot from along the left-wing boards.
Wilson responded for Washington 1:16 later to tie it 1-1 at 6:01 on a shot from the left face-off circle past Markstrom's glove. He tied the Capitals record for the longest goal streak to begin a season, matching Ovechkin (2013-14), Mike Gartner (1987-88) and Dennis Maruk (1979-80).
"Sometimes they're going in and you’ve got to enjoy it," Wilson said. "It's a tough league to score goals. It's a lot of good passes, a lot of good teammates, and I'm always happy to help this team win. We're coming together as a group and that's all that matters right now."
McMichael gave the Capitals a 2-1 lead at 10:14 on a rebound to the right of the net, and Ovechkin pushed it to 3-1 on a deflection from the slot at 14:18.
Hischier scored twice in 10 seconds in the opening 44 seconds of the second period for a 3-3 tie. His first goal came from the slot off a pass from Noesen at 34 seconds, and he got his second on a wrist shot from the bottom of the left face-off circle.
"It was captainlike; impressive," New Jersey coach Sheldon Keefe said. "It was unfortunate that we don't get rewarded for that and take off from there."