Kacey Musgraves set the bar high for the 50th anniversary season of Austin City Limits. The long-running television program will return this fall with a new slate of performances from veteran artists and newcomers alike — and Musgraves is first on the lineup. The musician’s hour-long set will premiere on PBS on Sept. 28 and includes a tender live performance of her Deeper Well single “Too Good to Be True.”

Musgraves begins the performance by commending the lively audience for their assistance on the previous song. But when she begins strumming...