The loss for Sounders FC (16-7-9, 57 points) snapped a three-game MLS winning streak and eliminates them from contention for the Supporters' Shield. With two regular season matches remaining Seattle sits second in the Western Conference, seven points behind the L.A. Galaxy.
Seattle played without its top three point producers: forward Fredy Montero and midfielders Alvaro Fernandez and Mauro Rosales. Montero was serving a suspension for yellow card accumulation. Rosales has been out since September 17 with an MCL sprain and Fernandez was on the bench after sustaining a mild concussion in Tuesday's U.S. Open Cup final.
Sounders FC central defender Jeff Parke was removed from the match at halftime with a concussion.
On the Union's opening goal, Gabriel Farfan dribbled to the end line and rolled a pass to Adu whose first-time shot went over the shoulder of a helpless Kasey Keller and into the roof of the net.
In the 70th minute, the visitors doubled their lead on a counterattack following a Seattle corner kick. Former Sounders FC forward Sebastian Le Toux took possession and ran at the defense before slipping the ball to the right side for a charging Carroll to shoot past Keller. It was Carroll's first goal of the year.
Le Toux's assist, his ninth, continues one of the hottest stretches for any player in the MLS this season, having scored or assisted in nine of his last 11 games.
Both teams combined for just four first-half shots. The best scoring opportunity for Seattle came in the 20th minute when a cross from Lamar Neagle was timed perfectly by Pat Noonan, but his volley shot went right into the arms of keeper Zac MacMath.
Sounders FC nearly got on the scoreboard first in the 53rd minute. Brad Evans chipped a shot from the top of the box over MacMath's head and hit the crossbar. MacMath finished with two saves to earn the shutout.
Seattle out-shot the Union 13-6 but managed only two shots on goal to Philadelphia's four. Sounders FC also had an 8-5 advantage in corners, all of theirs coming in the second half.
The game was played before the 48th consecutive sellout with an attendance of 36,304.
Both teams return to action next Saturday. Sounders FC will try again to clinch the West's second seed in their final MLS regular season home match against San Jose. Philadelphia hosts Toronto FC at PPL Park.