Dielectronic recombination resonances of Pb (79+) associated with 2s(1/2)-->2p(1/2) excitations were measured at the heavy-ion storage ring ESR at GSI. The fine structure of the energetically lowest resonance manifold Pb (78+)(1s(2)2p(1/2)20l(j)) at around 18 eV could partially be resolved, and rate coefficients on an absolute scale were obtained. A comparison of the experimental data with results of a fully relativistic theoretical approach shows that high-angular-momentum components up to j=31/2 significantly contribute to the total resonance strength demonstrating the necessity to revise the widespread notion of negligible high-angular-momentum contributions at least for very highly charged ions.