The result means RSL can win the aggregate series with a victory in Game 2 on Thursday at Rio Tinto Stadium.
Real Salt Lake and Seattle also played consecutive 0-0 draws in the regular season, although this one was far more meaningful for the visitors.
"It feels good, for sure," midfielder Ned Grabavoy said. "This is really a difficult place to play, [but] we kept it at zero."
The play that ended up in the postgame spotlight came in the 67th minute, when RSL keeper Nick Rimando came off his line to stop a cross intended for Seattle's Christian Tiffert.
Kyle Beckerman cleared the ball, but Tiffert's forearm struck Rimando in the eye as they collided.
Rimando went down and, as Sounder fans booed, he received attention for a gash that required three stitches after the game.
Backup goalie Kyle Reynish began warming up, but Rimando was able to finish what he started.
"We thought he was going to have to come out," RSL coach Jason Kreis said. "We thought it was going to be a laceration where they couldn't get the blood stopped.
"If that's the case, he has to come out. But they did a good job stopping the blood, and Nick continued on with a brave effort."
Other than some fans, no one in Seattle questioned Rimando's injury or the time he needed to get back his feet.
However, Seattle coach Sigi Schmid thought the delay slowed his team's momentum and, truthfully, Seattle's chances down the stretch were limited.
"It took us a while to get back into the flow," Schmid said. "I thought prior to that we were all over them. ... For them, it was a very timely injury because it helped slow the game."
The injury situation for both teams is muddled heading into Game 2.
RSL forward Fabian Espindola played the first half in Seattle but went to the bench with a hamstring issue.
"He was questionable coming into this game," Kreis said. "He gave us 45 minutes of everything he had and [then] made a smart decision to get himself off before he hurt himself more seriously."
Defender Jamison Olave didn't start for RSL because of a nagging hamstring injury, but he entered the game in the 76th minute for Kwame Watson-Siriboe.
"It was my ideal plan to try and get Olave into the game, to see if we could get him ready for next week," Kreis said. "But we were forced into that set because Kwame rolled his ankle and was limping around, and that's not the game you want to be limping around in."
For Seattle, leading scorer Eddie Johnson did not play because of an adductor strain. But he is expected to play in Game 2.
"Don't write us off," Sounder keeper Michael Gspurning said. "We are a good [road] team, too. So it will be a fun game."
MLS playoffs, Game 2
P Seattle at Real Salt Lake, Thursday at 7:30 p.m., Rio Tinto Stadium