With the victory, Sporting K.C. (12-6-3, 39 points, 1.86 points per game) clinched the top spot in the Western Conference for the MLS Cup playoffs.
It was the first win for SKC at Rio Tinto Stadium since 2013.
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Shelton scored in the 45th minute and Hurtado scored his fifth goal of the season shortly after half-time. Shelton's goal came after Ilie Sanchez attempted a shot from just outside the 6-yard box. It deflected off the heel of Shelton and then two RSL defenders.
Sporting KC keeper Tim Melia recorded his seventh clean sheet of the season with three saves.
A year after missing the MLS playoffs for the first time in nine seasons (11th place), Kansas City enjoyed the biggest one-season improvement in MLS history. SKC played like a team with plenty to play for, keeping Salt Lake on the defensive for most of the game.
With the momentum of Shelton's late first-half goal, SKC inserted Hurtado at half-time. The move paid off in the 48th minute when he connected from a sharp angle for a 2-0 lead. He received a beautiful feed from Jaylin Lindsey.
Hurtado now has five goals in just 15 appearances this season.
RSL (5-10-7, 22 points, 1.0 points per game) had been eliminated from playoff contention with their last loss.
Following a scrum in front of the RSL net in the 45th minute, Sanchez's and Shelton's effort led to a 1-0 Sporting K.C. lead at half-time. It was Shelton's fifth goal this season.
RSL controlled possession in the first half, sloppy as it was, but SKC had the most opportunities. Sporting had seven shots (three on goal), compared to two off-target attempts by RSL.