The emergence of graphene in recent years provides exciting avenues for achieving fast, reliable DNA/RNA sensing and sequencing. Here we explore the possibility of enhancing electronic fingerprints of nucleobases adsorbed on graphene by tuning the surface coverage and modifying molecular dipoles using first-principles calculations. We demonstrate that intermolecular interactions have a strong influence on the adsorption geometry and the electronic structure of the nucleobases, resulting in tilted configurations and a considerable modification of their electronic fingerprints in graphene. Our analysis reveals that the molecular dipole of the nucleobase molecules plays a dominant role in the electronic structure of graphene-nucleobase systems, inducing significant changes in the work functions and energy level alignments at the interface. These results highlight tunable control of the measured molecular signals in graphene by optimizing the surface contact between nucleobases and graphene. Our findings have important implications for identification and understanding of molecular fingerprints of DNA/RNA nucleobases in graphene-based sensing and sequencing methods.