Functional oxides are important materials for multiple applications in flexible and transparent electronics. Electrically contacting these oxides to form active channels is often challenging as they suffer significant alteration or instabilities when interfaced with metal electrodes. Here, we demonstrate a new scheme to electrically contact thin films of semiconducting zinc tin oxide (ZnSnO) that employs pre-patterned copper electrodes encapsulated by chemical-vapour-deposited graphene. Measurement of over more than 100 channels with varying geometry and nature of contact shows that the bulk resistivity of the ZnSnO channels with graphene/Cu composite is at least two orders of magnitude larger than the same films deposited directly on aluminium (Al) contacts. Moreover, the ZnSnO channels with Cu/graphene contacts showed nearly ohmic transport, in contrast to space-charge-limited conduction observed for other contacting schemes. Our results outline a new application of graphene in a step towards the development of alternative contacting strategies for oxide electronics.