Graphene-based sensors are exceptionally sensitive with high carrier mobility and low intrinsic noise, and have been intensively investigated in the past decade. The detection of individual gas molecules has been reported, albeit the underlying sensing mechanism is not yet well understood. Focusing on the adsorption of NO2, H2O, and NH3, we systematically investigate the chemirestistive response of molecular junctions with a pyrene core, which can be considered as a minimal graphenelike unit, within the framework of density functional theory and non-equilibrium Green's functions. We highlight the potential role of quantum interference (QI) in the sensing process, and we propose it as a paradigmatic mechanism for sensing. Owing to the open-shell character of NO2, its interaction with pyrene gives rise to a Fano resonance thereby triggering the strongest chemiresistive response, while the weaker interactions with H2O and NH3 result in lower sensitivity. We demonstrate that by exploiting destructive QI arising in the meta-substituted pyrene, it is possible to calibrate the sensor to enhance both its sensitivity and chemical selectivity by almost two orders of magnitude so that individual molecules can be detected and distinguished. These results provide a fundamental strategy to design high-performance chemical sensors with graphene functional blocks.