Field-effect transistors (FETs) with non-covalently functionalised molybdenum disulfide (MoS₂) channels grown by chemical vapour deposition (CVD) on SiO₂ are reported. The dangling-bond-free surface of MoS₂ was functionalised with a perylene bisimide derivative to allow for the deposition of Al₂O₃ dielectric. This allowed the fabrication of top-gated, fully encapsulated MoS₂ FETs. Furthermore, by the definition of vertical contacts on MoS₂, devices, in which the channel area was never exposed to polymers, were fabricated. The MoS₂ FETs showed some of the highest mobilities for transistors fabricated on SiO₂ with Al₂O₃ as the top-gate dielectric reported so far. Thus, gate-stack engineering using innovative chemistry is a promising approach for the fabrication of reliable electronic devices based on 2D materials.