She was 7 for 12 from the field in the second half and keyed a 14-0 fourth-quarter run with six points and three rebounds to help the Eastern Conference-leading Dream (8-3) run their winning streak to five games.
The Mystics (5-7) led much of the first three quarters. Washington, the least effective 3-point shooting team in the league, went 7 of 10 from long range en route to a 39-34 halftime lead. But the Mystics went cold for nearly 6 minutes in the fourth quarter under stiffer defensive pressure, and the Dream took advantage.
''We (made) them stop shooting, got in their faces,'' McCoughtry said. ''We would rather let them have 2s than 3s, so that kind of helped us.''
Atlanta held Washington to 1-of-7 shooting from 3-point range in the second half.
''I think our defense just stepped up a little bit; we started getting up on the shooters,'' Dream coach Michael Cooper said. ''We changed our pick-and-roll (defense) from one to another, and it really helped.''
Tiffany Hayes added 11 points for Atlanta, and Erika de Souza had 10 points and eight rebounds.
Rookie point guard Bria Hartley led Washington with 16 points, and Emma Meesseman added 15.
Mystics rookie Stefanie Dolson, who scored eight points on 4-of-5 shooting in 20 minutes, pushed the lead to 66-63 on a runner with 7:37 left. But the visitors went scoreless over the next 5:49.
McCoughtry's 11-foot fadeaway jumper from the left baseline with 6:39 left gave Atlanta the lead for good, 67-66.
Washington went 3 for 4 at the free-throw line, while Atlanta was 20 for 23, including 7 of 7 by McCoughtry.
''When the free-throw difference is 23-4, it's hard to make up for it,'' said Washington coach Mike Thibault, whose team lost for the fifth time in six games. ''They were aggressive, drove well ... they upped the aggression with the pressure, and we did a bad job responding.''