We present a novel implementation of supermassive black hole (SMBH) formation, dynamics, and accretion in the massively parallel tree+SPH code, ChaNGa. This approach improves the modeling of SMBHs in fully cosmological simulations, allowing for a more de- tailed analysis of SMBH-galaxy co-evolution throughout cosmic time. Our scheme includes novel, physically motivated models for SMBH formation, dynamics and sinking timescales within galaxies, and SMBH accretion of rotationally supported gas. The sub-grid parameters that regulate star formation (SF) and feedback from SMBHs and SNe are optimized against a comprehensive set of z = 0 galaxy scaling relations using a novel, multi-dimensional parameter search. We have incorporated our new SMBH implementation and parameter optimization into a new set of high resolution, large-scale cosmological simulations called Romulus. We present initial results from our flagship simulation, Romulus25, showing that our SMBH model results in SF efficiency, SMBH masses, and global SF and SMBH accretion histories at high redshift that are consistent with observations. We discuss the importance of SMBH physics in shaping the evolution of massive galaxies and show how SMBH feedback is much more effective at regulating star formation compared to SNe feedback in this regime. Further, we show how each aspect of our SMBH model impacts this evolution compared to more common approaches. Finally, we present a science application of this scheme studying the properties and time evolution of an example dual AGN system, highlighting how our approach allows simulations to better study galaxy interactions and SMBH mergers in the context of galaxy-BH co-evolution.