Real hit back with a good opportunity of their own when Plata latched on to the ball outside the box and drilled a left-footed strike towards the bottom corner, but Tim Melia made a good stop.
Salt Lake took the lead in the 34th minute when Javier Morales weaved his way through the Sporting defence before slotting an effort under Melia into the net.
The home side came close to doubling their lead just before the break as Abdoulie Mansally lifted the ball into the penalty area, but Plata's first-time strike clattered off the post.
In the second half, Kansas City drew level through an impressive strike from substitute Benny Feilhaber from distance as he curled an effort into the bottom corner.
The hosts were presented with the chance to go ahead when Olmes Garcia was brought down in the penalty area and a spot kick was awarded. Plata took the penalty and buried his strike past Melia.
Sporting pushed to get back into the game, but Attinella continued to be in inspired form as he made another good save to stop Peterson's close-range strike from finding the net.