Modified gravity based on the non-metricity scalar Q offers an effective alternative to ΛCDM, with several proposed f(Q) models successfully reproducing the late-time cosmic acceleration inferred from Type Ia supernovae. Current observational anomalies—such as hemispherical temperature asymmetry, the Hubble tension, cosmic voids, dipole modulation, and hints of anisotropic inflation—further motivate exploring departures from the cosmological principle. In this work, we study a broad class of f(Q) gravity models in an anisotropic Bianchi-I background to investigate their dynamical behaviour and cosmological viability. Using dynamical systems techniques, we identify stationary points of the cosmic evolution and classify their stability. Perturbative analyses are performed where applicable. Several fixed points arise only when both f(Q) modifications and anisotropies are considered, highlighting genuinely new cosmological features absent in isotropic or GR-based frameworks. In addition to recovering standard inflationary and late-time accelerating phases, we find that some models naturally support ultra-slow-roll inflation. For certain choices of f(Q), the shear evolves toward a non-zero constant, indicating a universe that gradually becomes more homogeneous, while other models allow complete isotropization depending on initial conditions. Special subclasses exhibit multiple stable attractors, each corresponding to distinct cosmological end-states. Our results demonstrate that f(Q) gravity in Bianchi-I spacetime provides a rich dynamical structure capable of addressing key cosmological tensions while offering novel predictions for both early- and late-time anisotropic evolution.