M-N-C catalysts have attracted considerable attention in the fields of energy storage and conversion as well as catalysis over the past decades. However, the current synthetic strategies for fabricating M-N-C catalysts via high-temperature pyrolysis unavoidably lead to a structural heterogeneity with the presence of a mixture of species including atomically dispersed M-Nx moieties and inorganic metal-containing particles, which not only decreases the atomic utilization but also clouds the accurate understanding of the nature of the catalytically active sites. Herein, we first report a straightforward and cost-effective preparation strategy for fabricating a Cu-N-C catalyst with atomically dispersed and coordinately unsaturated Cu-N2 moieties on hierarchically N-doped porous carbon (Cu1/NC-800) without formation of any metal-containing phases. Cu1/NC-800 exhibits outstanding catalytic performance for Glaser-Hay coupling of terminal alkynes under mild and sustainable conditions, which surpass those of the state-of-the-art catalysts. A broad set of (un)symmetrical aryl-aryl, aryl-alkyl, and alkyl-alkyl 1,3-diynes were selectively synthesized in high yields with good tolerance of various functional groups. More importantly, the Cu1/NC-800 could be easily reused with good maintenance of the activity and atomic dispersion of Cu in the structure. Experimental results and theoretical calculations reveal that the low N coordination number of single-atom Cu sites in Cu-N2 exhibit a preferential adsorption to terminal alkyne; meanwhile, the adjacent pyridinic N sites on the carbon matrix facilitate the deprotonation of the adsorbed alkyne to generate the key intermediate Cuδ-acetylide species, thus synergistically boosting the reaction. Therefore, this work not only provides an alternative facile synthetic strategy for fabricating atomically dispersed M-N-C catalysts but also represents a significant advance for accessing (un)symmetrical 1,3-diynes from Glaser-Hay coupling.