Kia Vaughn had 12 points and five rebounds and Bria Hartley added 11 points and four boards for the Mystics, who snapped a brief two-game slide on the heels of a 6-1 stretch.
Tina Charles put in 10 points for New York, which had won five of its last seven games coming in.
The Mystics scored 14 straight between the first and second periods and had already held a comfortable 37-22 advantage at the break. They blew the game wide open after outscoring the Liberty 27-13 in the third to take a 64-35 margin into the fourth. The Mystics made 9-of-14 shots in the period, led by Latta's eight points.
Washington held New York to just 28.8 percent shooting (17-of-59) from the field and scored 22 points off of its 16 turnovers.