Johnson headed home a corner kick to give Seattle a 25th-minute lead, and Juninho scored on a 24-yard free kick in first-half stoppage time.
Seattle (15-8-5), which saw its five-game winning streak halted, increased its lead in the Western Conference and Supporters' Shield standings to two points.
Los Angeles (13-10-6) jumped back into fourth place in the West, five points behind the Sounders.
Both teams were without their U.S. national team stars. Galaxy forward Landon Donovan sprained his ankle sustained last weekend and Sounders forward Clint Dempsey strained a calf in training this week.
The Galaxy were dominant after halftime, scoring a potential tiebreaking goal that was waved off and created little else that was concrete.
"We just weren't good enough in the final third of the field, with the final pass or our look at the goal, and it made a difference in the game," Los Angeles coach Bruce Arena said. "We obviously got the one goal called back. If that was a foul, then maybe Eddie doesn't get his goal in the first half. I thought (the officiating) was inconsistent, and in a tight game like that, those kinds of plays and calls are what decides the outcome."
Johnson scored on an open header from about 8 yards, losing Galaxy defender Omar Gonzalez as he started his run at the top of the box to get to Mauro Rosales' serve.
Johnson nearly scored another in the 39th, but Los Angeles goalkeeper Jaime Penedo leaped to grab his open shot in the box.
Juninho tallied with the final touch of the first half, bending a free kick from just above the semicircle inside the left post.
Rookie Gyasi Zardes forced a leaping save from Seattle goalkeeper Michael Gspurning with a blast toward the upper-right corner in the 19th minute, and he appeared to put the Galaxy ahead following a free kick 15 minutes into the second half, after Gonzalez headed Juninho's cross into the goalmouth. Referee Silviu Petrescu whistled the Galaxy for a foul, apparently on defender Todd Dunivant, while the ball was in the air.
"I think they had a little more possession than we had, for sure," Seattle coach Sigi Schmid said. "But I think that we had some very dangerous chances. ... I think we had opportunities to get our second goal, but that's the way it is. It's an end-to-end game, an exciting game for the fans, but it wasn't always the best soccer."