Pavol Regenda scored for the Sharks (13-12-3), who have alternated wins and losses in their past eight games (4-4-0). Yaroslav Askarov gave up four goals on 12 shots in the first period and was replaced by Alex Nedeljkovic, who made 15 saves.
"Snowballs out of control, really," Sharks coach Ryan Warsofsky said. "We turn one over on the power play, and it goes in the back of our net, and next thing you know, the momentum shifts dramatically."
Ovechkin jammed in a rebound at the left post to give the Capitals a 1-0 lead at 8:25 of the first period.
Sonny Milano pushed the Capitals' lead to 2-0 at 10:05 with a one-timer from the left circle. The Sharks unsuccessfully challenged the goal for goaltender interference.
Leonard roofed a rebound over Askarov from low in the left circle to make it 3-0 at 13:35.
"It's great to see the success for the team and put up as many goals as we did tonight," Leonard said. "Just try to play hard defensively for [Lindgren], because we know that every single night, what he's going to give for us."
Duhaime made it 4-0 with a short-handed goal at 17:07. After John Klingberg turned the puck over, Aliaksei Protas skated down the ice and dropped a pass to Duhaime, who beat Askarov by the blocker. Askarov was pulled for Nedeljkovic following the goal.
"They're mature. They're well-structured, and they play the right way," Sharks defenseman Mario Ferraro said. "They take care of their own end really well."
Ovechkin scored his second of the game on the power play at 2:41 of the second period. Leonard's cross-crease pass bounced to Ovechkin, and his one-timer beat Nedeljkovic over the glove.
"He did a great job of helping us build that lead," Carbery said of Ovechkin. "He's finding himself in and around the net. There's another example of how good his hands are in tight."