Kuznetsov had three assists, and Dylan Strome and John Carlson each had a goal and an assist for the Capitals (2-2-0), who trailed 4-2 entering the third. Marcus Johansson had two assists, and Darcy Kuemper made 26 saves.
"I thought in the third period we straightened out and played a really good third period -- maybe our best third period of the year and our best offensive period of the year," Washington coach Peter Laviolette said. "We were on the attack, and we were pushing the whole time."
Elias Pettersson had a goal and two assists, Quinn Hughes had two assists, and Thatcher Demko made 24 saves for the Canucks (0-3-0), who are on a season-opening five-game road trip. Vancouver coach Bruce Boudreau, a former Washington coach, was seeking his 600th NHL win.
"I think right now mentally weak would be a good assessment," Boudreau said when asked if Vancouver's issues were more physical or mental. "When you're on a roll, you're waiting for good things to happen. When you're in something like this, you're waiting for something bad to happen."
The Canucks, the first team in NHL history to lose their first three games of a season and blow a multigoal lead in each one, held a players-only meeting after the game.
"That's three games in a row now that we've had leads and outplayed teams and it's just unacceptable by us, it's unacceptable by myself and my leadership," Vancouver captain Bo Horvat said. "I hold myself accountable, I've got to be better. Luckily, we play [Tuesday] night (at the Columbus Blue Jackets), so we've got to have a short-term memory and go out there and do it."