The Mystics (16-11) scored the final six points after Brittney Griner's shot from the lane pulled the Mercury (17-12) within two with 2:43 to play.
Latta started the clinching run with a scoop shot at 1:38 after Emma Meesseman blocked Noelle Quinn's layup that could have tied it. Latta and Tierra Ruffin-Pratt made two free throws each in the closing seconds as Phoenix missed its last six shots and finished with 20 turnovers.
Meesseman had 14 points and Stefanie Dolson 10 points for the Mystics, who were without starting guard Kara Lawson because of back problems.
Leilani Mitchell led Phoenix with 16 points and Griner added 12, including her second dunk of the season and sixth of her career, the most in WNBA history.