Ivory Latta added 15 points and five assists for the Mystics.
Alex Bentley led the Sun with 17 points and Kelsey Bone added 14.
Latta's free throws gave Washington a three-point lead with 24.2 seconds remaining and, after Dolson's 12th rebound, off a miss by Thomas, Latta made two more to ice it.
Connecticut was without 2014 Rookie of the Year Chiney Ogwumike and Allison Hightower, both recovering from offseason knee surgery.
Washington led 44-40 at the half and immediately ran the lead to 12. Dolson started the run with a three-point play, Tierra Ruffin-Pratt nailed a 3-pointer, and Dolson hit a medium-range jumper to make it 52-40, while the Sun missed their first five shots after intermission.
The Mystics went cold at the start of the fourth quarter. The Sun went on an 8-0 run, then Chelsea Gray's running bank shot tied it at 57 with 8:07 left. Connecticut took a one-point lead with 3:26 left on a pair of free throws by Alyssa Thomas.