Drew Moor's header off a Nick LaBrocca corner kick had boosted the Rapids into a 1-0 lead after 60 scoreless minutes.
But Yedlin scored his first career MLS goal only 5 minutes later, using his head to put his own rebound past goalkeeper Clint Irwin and earn Seattle (7-7-4) a much-needed point.
The Sounders used the tally to break a two-game winless skid.
The Rapids (8-7-7), meanwhile, ran their unbeaten streak to five matches, staying within reach of a Western Conference playoff spot.
Swim Week Miami Beach 2014 [PHOTOS]