During evolution, organisms have gained functional complexity mainly by modifying and improving existing functioning systems rather than creating new ones ab initio. Here we explore the interplay between two processes which during evolution have had major roles in the acquisition of new functions: gene duplication and protein domain rearrangements. We consider four possible evolutionary scenarios: gene families that have undergone none of these event types; only gene duplication; only domain rearrangement, or both events. We characterize each of the four evolutionary scenarios by functional attributes. Our analysis of ten fungal genomes indicates that at least for the fungi clade, species significantly appear to gain complexity by gene duplication accompanied by the expansion of existing domain architectures via rearrangements. We show that paralogs gaining new domain architectures via duplication tend to adopt new functions compared to paralogs that preserve their domain architectures. We conclude that evolution of protein families through gene duplication and domain rearrangement is correlated with their functional properties. We suggest that in general, new functions are acquired via the integration of gene duplication and domain rearrangements rather than each process acting independently.