Reported is the asymmetric propargylic substitution (APS) reaction of 5H‐thiazol‐4‐ones using a Cu/Zn dual metal catalytic system and the APS reaction of 5H‐oxazol‐4‐ones using a Cu/Ti catalytic system. These reactions furnish functional‐group‐rich, terminal‐alkyne‐containing products with two vicinal stereocenters in high yields and with good to excellent diastereo‐ and enantioselectivities. This