Transcriptomic atlases have improved our understanding of the correlations between gene-expression patterns and spatially varying properties of brain structure and function. Gene-category enrichment analysis (GCEA) is a common method to identify functional gene categories that drive these associations, using gene-to-category annotation systems like the Gene Ontology (GO). Here, we show that applying standard GCEA methodology to spatial transcriptomic data is affected by substantial false-positive bias, with GO categories displaying an over 500-fold average inflation of false-positive associations with random neural phenotypes in mouse and human. The estimated false-positive rate of a GO category is associated with its rate of being reported as significantly enriched in the literature, suggesting that published reports are affected by this false-positive bias. We show that within-category gene-gene coexpression and spatial autocorrelation are key drivers of the false-positive bias and introduce flexible ensemble-based null models that can account for these effects, made available as a software toolbox.