A convenient Pd- and phosphine-free protocol for assembling internal alkynes from tertiary propargyl alcohols and (het)aryl halides has been developed. The proposed tandem approach includes the base-promoted retro-Favorskii fragmentation followed by Cu-catalyzed C(sp)-C(sp2) cross-coupling. The use of inexpensive reagents (e.g. a catalyst, additives, a base, and a solvent) and good functional group tolerance make the procedure practical and cost-effective. The synthetic utility of the method was demonstrated by a smooth alkynylation of vinyl iodides derived from natural steroidal hormones.