With the win, the Huskies take a 6-0-2 record into Pac-12 play when they travel to Stanford for a clash with the Cardinal on Thursday.
The Dawgs dominated the game, outshooting SMU 28-6 and holding a 15-0 advantage in corner kicks.
But SMU keeper Jaime Ibarra came up big time and again, making nine saves in keeping the Mustangs in the match.
SMU opened the scoring in the 22nd minute when Andrew Morales beat Washington keeper Ryan Herman for his second goal of the season.
After a scoreless second half and first overtime period, the Huskies finally broke through during the second overtime period in the 105th minute. Josh Heard received a through ball and crossed it across the face of the goal where Darwin Jones drilled it past Ibarra with his left foot for the game winning goal.
The goals were the second of the season for both Robertson and Jones. Herman made one save, improving to 3-0-1 on the season. The Huskies open Pac-12 play at Stanford on Thursday.