Emma Meesseman added 10 points for the Mystics (9-6), who won their third in a row.
A 3-pointer by Natasha Cloud sparked a 12-4 Washington run and gave the Mystics the lead for good.
Karima Christmas hit a 3-pointer with 1:02 to play, pulling Tulsa (10-8) within 70-67, but Meesseman answered with a layup and Kara Lawson had a steal and hit two free throws to give the Mystics a seven-point lead with 21 seconds left.
Christmas led Tulsa with 15 points while Plenette Pierson scored 14 and Odyssey Sims added 11. Courtney Paris tied a career-high with 19 rebounds.
Tulsa has lost four in a row.