Ryan Hollingshead scored the only goal of the game two minutes before halftime as the Toros are level on points with LAFC for fourth place in the Western Conference while SKC remain in third.
Jaylin Lindsay went close early on, firing over the bar while Hollingshead nodded over from a corner inside of the opening ten minutes.
Kansas City goalkeeper Tim Melia was alert to early danger as he saved from Franco Jara's 14th-minute shot. Tanner Tessman was next to try his luck, but the shot went well over.
FC Dallas was piling on the pressure as Jara tested Melia again, but the SKC keeper was up to the task. Finally, the hosts were on the board as Hollingshead met Bryan Reynolds' cross to send a right-footed shot off the par post and off of Melia's back.
Jara connected with Michael Barrios' pass at the top of the six-yard box only to push his close-range shot wide while Melia made a brilliant save to his left from Fafa Picault's shot from the edge of the area.
Jimmy Maurer denied SKC's Gadi Kinda in the 62nd minute. Eight minutes from time, Erik Hurtado wasted a clear chance, but he blazed his volley over the bar.
The visitors were in pursuit of an equalizer and three minutes from time, they thought they had it, Johnny Russell slotting home the rebound from Luis Martins' long-range volley, but referee Armando Villareal determined that Kinda fouled Maurer.
Peter Vermes: "That is a huge decision that is a game-changing call"
Following the match, Sporting Kansas City coach Peter Vermes spoke of the call that cost his team a point: "it's utterly ridiculous that that's not a goal. If the ball doesn't enter the goal, then it should be a penalty for the goalkeeper tackling Gadi Kinda and it would be a red card.
"The fact that it's not with VAR and everything else, I can not for the life of me understand how that call was not made. I was told explicitly by the referee that the VAR evaluated (it) and it also called a foul on our guy. I'm sorry, but on this one, there's no chance. If you've watched it yourself, there's absolutely zero chance."
FC Dallas: Tuesday, October 20 at SC Nashville (8:30pm ET | FS1, FOX Deportes, FOX Sports App, TSN 3/5)
Sporting Kansas City: Saturday, October 17 at Chicago Fire FC (3:30pm ET | Univison, TUDN, Twitter (English commentary), MLS Live on DAZN)