"We were the better team, I thought, for most of the game," Kane said. "We, obviously, weren't able to close it out. That's the bottom line."
Kane, who has four goals in his past two games, gave the Sharks a 1-0 lead with a power-play goal at 6:25 of the second period when his one-timer went through the legs of Barclay Goodrow.
Dowd scored 64 seconds later to tie it 1-1 with a one-timer under the right pad of Jones off a backhand pass from Brendan Leipsic.
Shortly after exiting the penalty box, Kane took a drop pass from Couture and beat Holtby with a wrist shot from the top of the right circle to make it 2-1 at 10:06.
Kane completed the hat trick to make it 3-1 at 16:49 with another power-play goal. Erik Karlsson's initial shot was blocked by Garnet Hathaway, but Kane got the rebound and quickly scored from the high slot.
San Jose went 2-for-4 on the power play after going 3-for-52 in its previous 22 games.
"We won the special teams," Boughner said. "Usually that's a recipe for a win, especially against the [Capitals], but it wasn't in the cards tonight."
The Capitals pulled to within 3-2 at 18:42 of the second when Oshie intercepted Marc-Edouard Vlasic's pass behind the net, circled out and sent a cross-crease pass to Vrana.