Seattle lost a four-game winning streak but stretched its unbeaten streak to six matches. Sounders forward Fredy Montero also failed to extend his nine-match point streak.
Keller posted his third consecutive shutout and eighth of the season. Thornton earned his fourth shutout.
Chivas USA's Mariano Trujillo and Seattle's Leo Gonzalez each picked up a red card in the 90th minute after a brief altercation.
Each team had 10 total shots.
With the point earned in the match, Seattle (8-8-5) moved ahead of Colorado into fourth place in the Western Conference standing while Chivas (5-10-4) remained in last.