Tayler Hill scored 19 points for the Mystics (3-2), who took control with a 21-0 run overlapping halftime in their first home game since May 14. Tianna Hawkins and Kristi Toliver each had 12 points.
Allie Quigley scored 17 points and Tamera Young had 16 for the Sky (1-4). Chicago fell back after not scoring for the opening 6:33 of the third quarter and was outscored 20-8 after trailing 47-38 at halftime.
Delle Donne, Hawkins and Hill all scored 10 points in the first half as Washington closed the second quarter with a 7-0 run in the final 47 seconds.
The Mystics opened the third quarter with the first 14 points, including eight combined from Hill and Delle Donne, for a 61-38 lead.
Courtney Vandersloot had 10 points in her Sky season debut after returning from an overseas commitment. She sank one of her two 3-pointers during a 12-0 spurt in the fourth quarter and Chicago closed within eight points with 55 seconds remaining but could get no closer.
Washington had lost the first two legs of a three-game road swing before winning 82-67 in Chicago on Wednesday.
Delle Donne, who spent her first four seasons with the Sky before requesting a trade this offseason, had 21 points and eight rebounds on Wednesday at Chicago. The 2015 WNBA MVP made all three of her free throw attempts on Friday and is 24 of 24 in the last four games.
The Mystics played their first game without Emma Meesseman, who led the WNBA in 3-point shooting last season. Meesseman left to join the Belgium national team in preparation for the FIBA World Championships.
Krystal Thomas replaced Meesseman in the starting lineup and grabbed 10 rebounds as the Mystics outrebounded the Sky 39-32.
Kahleah Copper, part of the Delle Donne trade, scored 10 points for the Sky.
Washington next hosts Connecticut on Wednesday after the Sky hosts the Sun on Sunday.