Luke Kunin scored for the Sharks (0-8-1), who are still seeking their first win and were shut out in their previous two games. Mackenzie Blackwood made 39 saves.
“Right now, we have such a thin margin for error,” San Jose coach David Quinn said. “Usually, if you only give up two goals, you like your chances, and right now, we’re really snakebit.”
Kunin gave the Sharks a 1-0 lead at 11:40 of the first period, banking a rebound off the skate of Kuemper from a low angle.
San Jose had gone 163:09 without a goal since the second period of a 3-1 loss at the Florida Panthers on Tuesday.
Strome tied the game 1-1 with a wrist shot from the point that beat Blackwood five-hole at 2:18 of the third.
“He’s just playing at a real high level right now,” Capitals coach Spencer Carbery said of Strome, who also won 21 of 27 faceoffs. “He’s putting himself in good spots. He’s playing a well-rounded game.”