Several studies have now shown evidence of association between common genetic variants and quantitative facial traits in humans. The reported associations generally involve simple univariate measures and likely represent only a small fraction of the genetic loci influencing facial morphology. In this study, we applied factor analysis to a set of 276 facial linear distances derived from 3D facial surface images of 2187 unrelated individuals of European ancestry. We retained 23 facial factors, which we then tested for genetic associations using a genome-wide panel of 10,677,593 single nucleotide polymorphisms (SNPs). In total, we identified genome-wide significant (p < 5 × 10−8) associations in three regions, including two that are novel: one involving measures of midface height at 6q26 within an intron of PARK2 (lead SNP rs9456748; p = 4.99 × 10−8) and another involving measures of central upper lip height at 9p22 within FREM1 (lead SNP rs72713618; p = 2.02 × 10−8). In both cases, the genetic association was stronger with the composite facial factor phenotype than with any of the individual linear distances that comprise those factors. While the biological role of PARK2 in the craniofacial complex is currently unclear, there is evidence from both mouse models and Mendelian syndromes that FREM1 may influence facial variation. These results highlight the potential value of data-driven multivariate phenotyping for genetic studies of human facial morphology.