Candace Parker scored five of her 19 points 82, in overtime.
Tina Thompson had 15 points and 10 rebounds, DeLisha Milton-Jones added 13 points and five steals while Noelle Quinn added 11 points off the bench for the Sparks, who have won three of four.
Crystal Langhorne had a game-high 28 points, Matee Ajavon added 14 points and DeMya Walker added 12 points for the Mystics, who have dropped six straight games.
Walker tied the game with just over a minute to play in regulation and a Kelly Miller three-pointer with 1:09 to play in overtime gave Washington an 80-79 lead.
Parker, though, answered with a layup and after a couple of Ajavon misses at the other end Ticha Penicheiro was fouled with 17.7 seconds to play and made both her free throws.
Marissa Coleman then missed a three at the other end and Thompson iced the game with two free throws with 11.3 seconds to play.