Abstract This work examines the impact of Finsler–Randers anisotropy on the internal structure, global properties, and stability of compact stellar configurations. Within the framework of Finslerian gravity, we construct an anisotropic relativistic stellar model to investigate how departures from Riemannian geometry General Relativity (GR) alter the fundamental physical characteristics of ultra-dense matter. A detailed comparison with the corresponding GR solution is carried out to elucidate the role of Finslerian anisotropy in modifying density and pressure profiles, stellar compactness, and equilibrium behavior. Analysis of the Mass–Radius (M-R) and Moment of Inertia-Mass (I-M) curves indicate that Finslerian corrections substantially increase the maximum supported mass, reaching up to $2.28\,M_{\odot }$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mn2.28</mml:mn> mml:mspace/ mml:msub mml:miM</mml:mi> mml:mo⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> , and the maximum moment of inertia, attaining $3.38 \times 10^{45}\,\text {g\,cm}^2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mn3.38</mml:mn> mml:mo×</mml:mo> mml:msup mml:mn10</mml:mn> mml:mn45</mml:mn> </mml:msup> mml:mspace/ mml:msup mml:mtextg,cm</mml:mtext> mml:mn2</mml:mn> </mml:msup> </mml:mrow> </mml:math> compared to their GR counterparts. We further analyze the M-R and I-M relations in the context of current observational constraints from neutron-star pulsars, allowing us to predict the maximum admissible mass and radius compatible with recent astrophysical data of massive pulsars PSRJ0740+6620 , PSRJ0952-0607 and GW observational events GW190814 and GW170817 . This enhancement underscores the role of geometric Finslerian anisotropy in reinforcing the structural stability of ultra-dense stellar configurations. The physical viability of the model is rigorously tested through standard energy conditions, causality requirements, hydrostatic equilibrium governed by the generalized Tolman–Oppenheimer–Volkoff equation, and multiple stability diagnostics, including the adiabatic index, Harrison–Zeldovich–Novikov criterion, equation of state behavior, and cracking analysis. Our results indicate that Finsler–Randers anisotropy plays a non-trivial role in shaping both the structural and stability features of compact stars, offering a viable geometric extension to GR for describing high-density astrophysical systems.