Martins' left-footed shot off an assist from Mario Martinez was his fourth goal of the year and provided all the offense the Sounders would need.
Chivas USA's Mario de Luna netted an own-goal 11 minutes later as Seattle (5-4-3) continued a rebound from a poor start, pulling to within two points of Colorado for fifth place in the Western Conference.
The Goats (3-8-2) saw their winless streak extended to eight games.
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]
Wisconsin business offering 'therapeutic cuddling' forced to close