Kia Vaughn had 10 points and a career-high 13 rebounds for Washington (5-8), which lost its third straight and sixth in seven. Kara Lawson added 14 points.
Showing no signs of caution, Augustus made a 3-pointer, then scored on a spin move for a bucket in the opening minutes.
"She's a leader," Moore said. "She just sets the way and leads the way of how you carry yourself when you play through pain. It fires me up and everybody else up."
Eight points by Moore -- including two 3-pointers -- and six points by Augustus keyed a 26-7 run bridging the first and second quarters to give the Lynx a 35-18 lead.
Kara Lawson made two 3s and Bria Hartley scored four points as Washington countered with a 16-4 run to get within five points before Minnesota scored the final four points of the quarter for a 43-34 halftime lead.
Moore scored on a turnaround, Augustus hit a jumper and Moore made a driving layup to put the Lynx up 55-42 in the third quarter. A 3 by Moore and a jumper from Augustus put Minnesota up 65-51 early in the fourth.
"I'll take Seimone on a bad day any day of the week, twice on Sunday," Minnesota center Janel McCarville said.
Washington pulled within nine on a jumper by Hartley with 3:08 to play, but got no closer.
"I'm not walking out of here as frustrated as you might think after a loss just because the things we've been working to get better at we did a little better," Mystics coach Mike Thibault said. "We've been turning it over too much and we didn't tonight."
The Mystics had nine turnovers, just two in the second half.
However, long-distance shooting remains an issue. Washington, which entered the game shooting a league-worst 29.8 percent from beyond the arc, was 5 for 23.
"We're awful right now," Thibault said. "We have good 3-point shooters who are not making shots. ... Teams right now have decided they're going to make us shoot those shots."
Gutting out a win at home was crucial for the struggling Lynx, who host Indiana on Sunday in the last of a six-games-in-10-days stretch.
"We've got a tired group. We feel like we're running in mud and we told them we just got to keep fighting and get through it," Lynx coach Cheryl Reeve said.