Numerous studies have evaluated the publication performance of universities worldwide, but studies examining intra-institutional performance still remain scarce. In this paper, as a case study, we provide an in-depth quantitative-qualitative analysis of University of Belgrade (UB) leading institutions performance. The results show that the UB scientific institutes, faculties of sciences and mathematics, together with the Faculty of Medicine and several faculties of technology and engineering sciences exhibit excellent scientific results. The Faculty of Medicine and Institute Vinča lead the way in terms of number of published papers, while Institute of Physics excels when taking into account the quality of journals. Results pointed out that the Faculty of Technology and Metallurgy, besides the number of papers, has a strong showing in terms of citation metrics. In addition, using a network graph we present collaboration patterns within the UB. This analysis may be a step in the right direction towards a model for evaluating and ranking institutions within a particular university.