Moore made a pair of free throws to tie it at 72 with 1:50 left and hit a baseline jumper with 1:09 left to give the Lynx (10-6) the lead for good.
The Wings (7-8) took their first lead since the middle of the second quarter when Allisha Gray capped an 8-0 run to make it 72-70 with 2:12 left.
The Lynx built a 48-33 lead with an 8-0 run to open the third quarter. The Wings cut the deficit to 56-55 before the end of the period.
Skylar Diggins-Smith led Dallas with 16 points and Gray scored 15. Wings center Liz Cambage left the game near the beginning of the third quarter with an eye injury and did not return. Cambage finished with 14.