Washington blew a 2-0 lead in the third period, but Evgeny Kuznetsov completed his second NHL hat trick with a power-play goal with 4:53 left to tie it 3-3.
"Nobody was panicking, nobody was reaching," Kuznetsov said. "It was always positive. We always believe in each other."
John Carlson had two assists, and Vitek Vanacek made 23 saves for the Capitals.
Bo Horvat scored twice, Quinn Hughes had a goal and two assists, and Demko made 30 saves for the Canucks (29-23-7), who lost for the first time in four games (3-0-1) and second time in the past eight (6-1-1).
"Obviously we're happy to fight back at the end of the third but ultimately we wanted those two points, and all the points from here on out are going to be huge for us," Horvat said. "I thought it was great character by us to come all the way back and get that point. Just unfortunate that we couldn't get the job done."
Canucks forward J.T. Miller had two assists to extend his point streak to 11 games (23 points; seven goals, 16 assists).
Kuznetsov gave Washington a 1-0 lead at 5:34 of the first period when Nick Jensen shot the puck around the end boards and it hit a stanchion behind the Vancouver net, bounced out front and in off Kuznetsov's shoulder.
Kuznetsov made it 2-0 at 6:17 on a power-play goal that looked like it might move Ovechkin past Jagr. Ovechkin's one-timer hit the post, bounced off Demko and was wobbling into the net before Kuznetsov swiped it in off the goal line.
"'Kuzy's got to put that in," Laviolette said. "They've got a defender right there ready to swat it out. I'm not sure if it gets there or not and if he doesn't touch it, the guy comes in and knocks it out of the crease, so he 100 percent did the right thing. Alex will get his goal. He needed to put that one in the back of the net to make sure."