Gene expression in multiple individual cells from a tissue or culture sample varies according to cell-cycle, genetic, epigenetic and stochastic differences between the cells. However, single-cell differences have been largely neglected in the analysis of the functional consequences of genetic variation. Here we measure the expression of 92 genes affected by Wnt signaling in 1,440 single cells from 15 individuals to associate single-nucleotide polymorphisms (SNPs) with gene-expression phenotypes, while accounting for stochastic and cell-cycle differences between cells. We provide evidence that many heritable variations in gene function--such as burst size, burst frequency, cell cycle-specific expression and expression correlation/noise between cells--are masked when expression is averaged over many cells. Our results demonstrate how single-cell analyses provide insights into the mechanistic and network effects of genetic variability, with improved statistical power to model these effects on gene expression.