Fredy Montero scored the lone goal for the Sounders, who lost for the first time at home this season.
The Sounders had allowed a league-low nine goals entering the match, but fell behind 2-0 by halftime.
Russell opened the scoring in the 31st minute on a free kick from just outside the top of the 18-yard box. His left-footed shot curled around the wall of Sounders defenders and just out of the reach of goalkeeper Stefan Cleveland before ricocheting high off the left post and into the net.
Kansas City doubled its advantage in the 42nd minute on a counterattack following a Seattle corner kick. Khiry Shelton and Gadi Kinda moved the ball down the field to the top of the 18-yard box before Kinda dropped a pass for Salloi, whose 20-yard shot soared into the upper right corner of the net.
The Sounders pulled within 2-1 on Montero's goal in the 51st minute. Kelyn Rowe's cross from the right wing found Reed Baker-Whiting in the penalty area, but the ball was knocked away by a sliding defender. The ball bounced to Montero, who put a left-footed shot from 7 yards out into the lower left corner.
Kansas City restored its two-goal lead in the 72nd minute. Duke, who came on as a substitute two minutes earlier, took a cross-field pass from Graham Zusi and put a sliding volley into the net from about 10 yards out. It was the first MLS goal for the 20-year-old from Overland Park, Kan.
SKC goalkeeper Tim Melia made five saves, including a diving stop on Montero's bicycle kick in the 26th minute. Melia also denied a close-range shot from Seattle's Raul Ruidiaz, the league's leading scorer, in second-half stoppage time.