To address the challenges in controlling magnetic levitation systems — marked by multi-disturbance environments, strong coupling, and nonlinear dynamics — that are prone to model uncertainties and external perturbations, this paper introduces an integral global fast terminal sliding mode control (IGFTSMC) methodology integrated with an extended state observer (ESO). Initially, a single-point F-rail magnetic levitation experimental setup is developed, and its dynamic model is systematically formulated. A novel global fast terminal sliding manifold is devised to guarantee finite-time convergence, while incorporating an integral term of the air-gap error into the sliding surface. This integration mitigates steady-state errors and enhances trajectory tracking precision. Subsequently, the exponential reaching law is optimized to satisfy levitation operational constraints. The conventional sign function, prone to chattering, is supplanted by a smooth, continuously differentiable hyperbolic tangent function, effectively damping undesired oscillations. Concurrently, embedding the absolute value of the sliding variable enables balanced optimization between chattering suppression and convergence rapidity. Furthermore, the ESO is embedded within the augmented sliding mode framework to dynamically estimate and counteract system uncertainties and exogenous disturbances. This integration bolsters the system's robustness and accelerates dynamic responses. Comparative simulations and physical experiments validate the proposed approach. Results highlight superior performance of the IGFTSMC over existing methods in terms of control precision, disturbance rejection, and convergence velocity.