We present the Mufasa suite of cosmological hydrodynamic simulations, which employs the Gizmo meshless finite mass (MFM) code including H 2 -based star formation, nine-element chemical evolution, two-phase kinetic outflows following scalings from the Feedback in Realistic Environments zoom simulations, and evolving halo mass-based quenching. Our fiducial (50h −1 Mpc) 3 volume is evolved to z = 0 with a quarter billion elements. The predicted galaxy stellar mass functions (GSMF) reproduces observations from z = 4 → 0 to 1.2σ in cosmic variance, providing an unprecedented match to this key diagnostic. The cosmic star formation history and stellar mass growth show general agreement with data, with a strong archaeological downsizing trend such that dwarf galaxies form the majority of their stars after z ∼ 1. We run 25h −1 Mpc and 12.5h −1 Mpc volumes to z = 2 with identical feedback prescriptions, the latter resolving all hydrogen-cooling halos, and the three runs display fair resolution convergence. The specific star formation rates broadly agree with data at z = 0, but are underpredicted at z ∼ 2 by a factor of three, re-emphasizing a longstanding puzzle in galaxy evolution models. We compare runs using MFM and two flavours of Smoothed Particle Hydrodynamics, and show that the GSMF is sensitive to hydrodynamics methodology at the ∼ ×2 level, which is sub-dominant to choices for parameterising feedback.