The Sounders (6-2-1) won their MLS-leading fourth straight game, extended their unbeaten streak to five and took the overall league lead with 19 points.
Philadelphia (1-4-5) saw its winless streak extended to eight games (0-4-4), tying a club record that was first set in 2011 and matched in 2012.
Pappa's corner kick from the right side floated into the penalty area just outside the 6-yard box. Marshall ran and headed it high into the net over goalkeeper Zac MacMath for his first of the year.
The Union took the lead late in the 13th minute when a long free kick into the penalty area went into the Seattle net off of Brad Evans' head.
The own goal was the result of a free kick by the Union's Cristian Maidana about 40 yards upfield and slightly toward the right side. He drove it into the box, where teammate Maurice Edu and Seattle's Evans both went up for it. The ball flew into the right side of the net and originally was credited to Edu, but was changed moments later to an own goal off of Evans.
Obafemi Martins tied it for Seattle in the 61st minute, his fourth goal of the season.
The Sounders created multiple opportunities to tie it before halftime, none better than Osvaldo Alonso's penalty kick early in the 40th minute after Philadelphia's Amobi Okugo was called for a hand ball in the box. Alonso went toward the right post, but MacMath dived to his left and blocked it.
Evans started the play that led to the tying goal when he headed a short ball into the penalty area. Martins caught up with it at the penalty spot, took it to the top of the 6-yard box and shot into a wide-open right side of the net for his fourth of the season.
The Sounders put their winning streak on the line next week against FC Dallas. The game is scheduled for Wednesday at CenturyLink Field.