Diego Ferrerya, who plays for local club Tigres, scored less than eight minutes after coming on as a halftime substitute. Rosario scored the tying goal a few minutes later on a penalty kick (the name of the goalscorer isn't available).
Sounders FC midfielder Fredy Montero set up the goal with a square pass after being played into space by Stephen King. Ferreya placed his shot from about 15 yards out into the upper corner.
Defender Jhon Kennedy Hurtado played his first match for the club after joining the team in Argentina from his native Colombia on Wednesday.
"It was also good for him to get his first minutes," said Coach Sigi Schmid. "Obviously fitness is something he's got to acquire, he'll improve on that. But you could see his closing speed and one-on-one defending ability was very good."
Goalkeeper Chris Eylander played the full 70 minutes in goal and Ely Allen, a Washington native waived by the Galaxy in midweek, arrived just four hours before kickoff and played the final 16 minutes.
"We forced ourselves to do a lot of defending in the first half that we didn't need to do," said Schmid. "You live and learn and the guys learned a valuable experience in the game today. And for us as coaches it was valuable because we see who steps in those situations and who doesn't."
Seattle plays River Plate on Thursday in the final game of its visit to Argentina and will fly home later that night.