Corey Perry scored his first goal of the season and had an assist on Henrique's game-winning goal, and Ryan Getzlaf had two assists for Anaheim.
Ovechkin said he wasn't surprised the Ducks scored five goals after combining for nine in their previous nine games (1-8-0).
"They have some talent," he said. "They have some experience over there."
John Carlson had a goal and an assist, and Braden Holtby made 34 saves for Washington (32-20-7), which is 2-2-1 in its past five games and trails the New York Islanders by five points for first place in the Metropolitan Division.
"These are important games and important points," Carlson said. "Everything is so tight right now that we've got to work through this and start getting hot quickly."
The Ducks scored two power-play goals in the third period before Silfverberg made it 5-2 at 14:55 with his Anaheim-leading 15th goal.
Henrique tapped in the puck during a scramble in front of the net for a 3-2 lead 37 seconds into the period. Perry, playing his eighth game after he missed the first four months of the season with a knee injury, scored at 3:40 for a 4-2 lead.
"We played a desperate team that worked, and they were more detailed than us," Capitals coach Todd Reirden said. "Those are a couple areas that have been sources of areas that we need to improve on, and tonight it kind of reared its head in terms of how the goals ended up in our net."
Ovechkin drew a tripping penalty against Hampus Lindholm at 2:58 of the first period and scored on a one-timer from the left face-off circle off a pass from Carlson to give the Capitals a 1-0 lead at 4:58.
It is the eighth time in Ovechkin's 13 full NHL seasons that he reached 40 goals first.
Henrique tied the game 1-1 at 6:26 of the second period, ending a 139:56 goal drought for Anaheim.
Silfverberg redirected a pass from Henrique for a 2-1 lead at 14:07.
Carlson scored on a shot from the point at 17:01 of the second to tie it 2-2.
The Ducks won both games of their season series with the Capitals for the first time since the 1999-00 season.