Knowledge of the number and nature of genetic changes responsible for adaptation is essential for understanding and predicting evolutionary trajectories. Here, we study the genomic basis of compensatory adaptation to the fitness cost of fungicide resistance in experimentally evolved strains of the filamentous fungus Aspergillus nidulans. The original selection experiment tracked the fitness recovery of lines founded by an ancestral strain that was resistant to fludioxonil, but paid a fitness cost in the absence of the fungicide. We obtained whole-genome sequence data for the ancestral A. nidulans strain and eight experimentally evolved strains. We find that fludioxonil resistance in the ancestor was likely conferred by a mutation in histidine kinase nikA, part of the two-component signal transduction system of the high-osmolarity glycerol (HOG) stress response pathway. To compensate for the pleiotropic negative effects of the resistance mutation, the subsequent fitness gains observed in the evolved lines were likely caused by secondary modification of HOG pathway activity. Candidate genes for the compensatory fitness increases were significantly overrepresented by stress response functions, and some were specifically associated with the HOG pathway itself. Parallel evolution at the gene level was rare among evolved lines. There was a positive relationship between the predicted number of adaptive steps, estimated from fitness data, and the number of genomic mutations, determined by whole-genome sequencing. However, the number of genomic mutations was, on average, 8.45 times greater than the number of adaptive steps inferred from fitness data. This research expands our understanding of the genetic basis of adaptation in multicellular eukaryotes and lays out a framework for future work on the genomics of compensatory adaptation in A. nidulans.