Patrick Rismiller and Matthew Carle scored in regulation and Evgeni Nabokov stopped 24 shots for San Jose, which ended a three-game losing streak and beat Washington for the 10th straight time.
Shaone Morrisonn and Brian Sutherby scored for the Capitals, who have not beaten the Sharks since Feb. 20, 1999. Washington has dropped five straight overall.
Matt Pettinger scored in the shootout for Washington, but Nabakov stopped both Alex Ovechkin and Alexander Semin. Cheechoo then ended the shootout with a backhand shot past Brent Johnson.
Morrisonn and Sutherby scored less than a minute apart midway through the first as Washington registered goals on two of its first four shots.
After the Sharks stopped a 2-on-2 rush, Morrisonn scored from the left point, ending a 43-game goal drought at 9:52. When defenceman Kyle McLaren failed to Jamie Heward's rebound in front of the crease 49 seconds later, Sutherby knocked in the loose puck for a 2-0 lead.
Rismiller converted Mike Grier's pass, capping a 3-on-2 break with his fifth goal at 17:02.
Carle's power-play goal with 14:11 remaining in the third tied the score. Carle finished off a three-shot flurry by tapping in the puck as it rolled along the goal-line.
Notes: The Capitals have played five overtime games in their last eight . . . San Jose scratched C Patrick Marleau (food poisoning), but Pavelski returned after missing eight games with a foot injury . . . Capitals C Kris Beech rejoined the lineup after nine consecutive games as a healthy scratch . . . Ovechkin has scored one goal in nine games, the worst slump of his brief NHL career.