Tiffany Hayes and Renee Montgomery each scored 12 points for the Dream.
The series shifts back to Atlanta for the finale of the best-of-5 series on Tuesday.
The teams split the first two games in Atlanta, though Washington held a double-digit lead in Game 2 before losing.
Delle Donne averaged 29.5 points and 13.5 rebounds in Atlanta. The Mystics have never reached the WNBA finals in the franchise's 21 seasons.
Atlanta remains one victory away from the franchise's fourth finals appearance and first since 2013. Brittney Sykes and Jessica Breland also scored 12 points.
The Mystics raced out to a 26-12 lead in the second quarter and entered halftime up 44-35. Toliver, who had only seven points on 3 of 15 shooting in Game 3 topped all scorers with 12 points in the first half.
Delle Donne's second of three 3-pointers stifled Atlanta's momentum after the Dream's 10-0 run cut Washington's lead to 62-57 with 2:04 left in the third.