The stability of cationic gold clusters doped with one transition metal atom was investigated by a mass spectrometric analysis of fragments resulting from high fluence irradiation of a cluster beam. Strongly enhanced abundances are found for Au5X+, X = V, Mn, Cr, Fe, Co, Zn, which implies that these species are far more stable towards fragmentation than their neighbouring cluster sizes. Here we interpret the enhanced stability of these clusters within a shell model approach for two-dimensional (2D) systems: the number of delocalized electrons in Au5X+ is six, which is a magic number for 2D systems. Quantum chemical calculations for AuNZn+ (N = 2-6) predict planar structures that are stabilized by the influence of the dopant atom. Also, the main features of the calculated molecular orbitals are well reproduced by a simple electron-in-a-box model. The present report constitutes the first observation of 2D magic numbers in size dependent properties of metal clusters.