Walker closed with a 2-under 70 to finish at 11-under 277 at TPC San Antonio, a 35-minute drive from his home. The former Baylor player won the Sony Open in Hawaii by nine shots in January and had five victories in the past two seasons.
Spieth also finished with a 70, making four late birdies. The 21-year-old Dallas player was coming off a playoff victory two weeks ago at Innisbrook.
FedEx Cup champion Billy Horschel was third at 4 under after a 71.
