Josh Manson scored nine seconds into the second period to tie it 1-1, jamming in a loose puck in the crease after Milano's initial shot hit the post and deflected off Samsonov.
"We gave up too much space," Capitals coach Peter Laviolette said. "We gave up too many point-blank chances right in front of our own net, and just things we haven't done as a group."
Carl Hagelin scored his first of the season put the Capitals back in front 2-1 at 3:58, converting off a cross-slot pass from Lars Eller.
"Sergei Ovechkin (Alex's son) actually called it yesterday," Hagelin said. "He got a bobblehead from me, and he told 'Ovi' that I was going to score, and then Ovi told me this morning. You have to listen to the little guy."
Milano batted in the rebound of Zegras' shot near the left post to tie it 2-2 at 13:35.
"They played extremely well," Eakins said of the Milano-Zegras-Rickard Rakell line. "They were in sync and they are all dancing to the same tune. They have a great rhythm going. … I thought all three of those guys were excellent."
Vinni Lettieri
gave the Ducks a 3-2 lead at 15:29 with a one-timer off a pass from Cam Fowler on a 3-on-2 rush.
Carlson then tied it 3-3 at 19:37. Ovechkin intercepted a clearing attempt by Manson and left a drop pass for Carlson, who scored on his own rebound at the top of the crease.
"It took us maybe a little bit to get going in the first period, but once we found our game, we were playing right with those guys," Zegras said. "We just tried to kind of play their game. It comes down to a shootout, so you can't really hang your head on that, but it would have been nice to get the extra point, for sure."
NOTES:Ovechkin has scored 41 points (20 goals, 21 assists) in 26 games this season, tying Dennis Maruk (1981-82) for the fastest to reach 40 points in a season in Capitals history. … Washington is 9-1-4 at home. … Zegras is the fourth rookie in the past 25 years to record multiple assists in three straight games, joining Mathew Barzal (2017-18), Artemi Panarin (2015-16) and Patrick Kane (2007-08).