Real Salt Lake (7-7-8) won its second straight game after a four-game winless stretch. Sporting KC (9-4-6) had its three-game winning streak stopped.
Morales dribbled around three defenders with some nifty footwork and sent a shot past goalkeeper Tim Melia in the 34th minute. Real Salt Lake's possession started with a long goal kick, followed by three straight headers to find Morales' feet. Plata's well-placed penalty kick came after Olmes Garcia was tripped up in the box by Melia after a long run from beyond midfield.
Plata and Morales have scored in two consecutive matches.
Kansas City's Benny Feilhaber sent in a perfectly placed ball from distance in the 50th minute — just moments after entering as a second-half sub. Sporting's Jacob Peterson had a goal disallowed in the 45th after he was whistled for being offside. He lost a one-on-one battle with goalkeeper Jeff Attinella in the 65th and had a close-range shot saved in the 76th.