The potential of copper(I)-zeolite catalysis was evaluated in the three-component KA2-coupling mediated synthesis of α-tertiary propargylamines. Our archetypal copper(I)-doped zeolite CuI-USY proved to be efficient under ligand- and solvent-free conditions at 80 °C. Usable up to four times, this catalytic material enables the coupling of diverse ketones, alkynes, and amines with a broad functional group tolerance. A decarboxylative and a desilylative version, respectively, involving an alkynoic acid and trimethylsilylacetylene as alkyne surrogates, was also set up to bypass selectivity issues and/or to access α-tertiary propargylamines that are unattainable under standard KA2 conditions. Interestingly, the KA2-type coupling reactions were successfully linked to other CuI-catalyzed reactions, thus resulting in sequential one-pot processes under full CuI-USY catalysis.