The application of Multi-Objective Evolutionary Algorithms (MOEAs) is often constrained when addressing computationally expensive Multi-Objective Optimisation Problems (MOOPs). To mitigate this, we propose a dominance-based surrogate classifier that can be integrated into a MOEA to steer the algorithm towards viable (potentially non-dominated) solutions, thereby facilitating faster convergence. This surrogate classifier is paired with a simple, yet effective data labelling mechanism, which assigns a label of 1 to non-dominated solutions and a label of 0 to dominated solutions within a generation. Experimental results demonstrate that a surrogate classifier guided NSGA-II achieves faster convergence compared to the standard NSGA-II across 31 well-known benchmark problems.