Washington's best chance to take the lead in regulation came with a little more than a minute left in the third period when Mike Richards intercepted Anaheim defenseman Cam Fowler's errant cross-ice pass and cut through the slot all alone, but Gibson was able to make the save.
Gibson made 31 saves in his first loss in five games.
"He was spectacular, there's no doubt," Boudreau said. "Our goaltending has been spectacular for a while now. He had a really good game."
The Ducks failed to score a power-play goal for the first time in 12 games. They were 19-for-42 (45.2 percent) with the man-advantage during their winning streak.
Capitals forward Alex Ovechkin, whose 41 goals lead the NHL, didn't have a shot on goal for more than 40 minutes, with his first coming at 3:21 of the third period. He had three more in the next 2:31 and another in overtime.
Anaheim's third line of Andrew Cogliano, Ryan Kesler and Silfverberg effectively limited Ovechkin's impact.
"It was the Kesler line," Boudreau said. "They still made some nice plays, and you could still see the skill and the danger every time he had the puck, but I thought we did a nice job against him."
Although Boudreau wasn't necessarily happy with Anaheim's level of execution, the Ducks were pleased with how they matched up against the Capitals, who are first in the NHL standings with 102 points.
"We go to a shootout and it's a flip of a coin," defenseman Kevin Bieksa said. "We played against -- in my opinion, and a lot of people's opinion -- the best team of the East. We matched up well against them. You're not going to win every game, but we played well tonight."