The Wings announced several hours after the game that coach Fred Williams was being relieved of his duties following an eighth straight loss.
The Mystics (20-11) pulled away to a 51-37 halftime lead with a 25-9 run to close the second quarter and extended the advantage to 70-46 on Atkins' 3-pointer with 3:18 left in the third.
The Wings (14-17) rallied to 77-71 on Kayla Thornton's 3-pointer with 7:20 left in the game but got no closer.
Kristi Toliver added 17 points with a trio of 3s for Washington. Atkins hit all five of her 3-point attempts and Delle Donne was 3 of 5.
Dallas has a one-game lead over Las Vegas (13-18) for the final playoff spot, with each having three games remaining.