Single-cell RNA-seq's (scRNA-seq) unprecedented cellular resolution at a genome-wide scale enables us to address questions about cellular heterogeneity that are inaccessible using methods that average over bulk tissue extracts. However, scRNA-seq data sets also present additional challenges such as high transcript dropout rates, stochastic transcription events, and complex population substructures. Here, we present a single-cell RNA-seq analysis and klustering evaluation (SAKE), a robust method for scRNA-seq analysis that provides quantitative statistical metrics at each step of the analysis pipeline. Comparing SAKE to multiple single-cell analysis methods shows that most methods perform similarly across a wide range of cellular contexts, with SAKE outperforming these methods in the case of large complex populations. We next applied the SAKE algorithms to identify drug-resistant cellular populations as human melanoma cells respond to targeted BRAF inhibitors (BRAFi). Single-cell RNA-seq data from both the Fluidigm C1 and 10x Genomics platforms were analyzed with SAKE to dissect this problem at multiple scales. Data from both platforms indicate that BRAF inhibitor-resistant cells can emerge from rare populations already present before drug application, with SAKE identifying both novel and known markers of resistance. These experimentally validated markers of BRAFi resistance share overlap with previous analyses in different melanoma cell lines, demonstrating the generality of these findings and highlighting the utility of single-cell analysis to elucidate mechanisms of BRAFi resistance.