The electrical properties of reduced graphene oxide (rGO) have been previously shown to be very sensitive to surface adsorbates, thus making rGO a very promising platform for highly sensitive gas sensors. However, poor selectivity of rGO-based gas sensors remains a major problem for their practical use. In this paper, we address the selectivity problem by employing an array of rGO-based integrated sensors instead of focusing on the performance of a single sensing element. Each rGO-based device in such an array has a unique sensor response due to the irregular structure of rGO films at different levels of organization, ranging from nanoscale to macroscale. The resulting rGO-based gas sensing system could reliably recognize analytes of nearly the same chemical nature. In our experiments rGO-based sensor arrays demonstrated a high selectivity that was sufficient to discriminate between different alcohols, such as methanol, ethanol and isopropanol, at a 100% success rate. We also discuss a possible sensing mechanism that provides the basis for analyte differentiation.