Magnetic molecules are potential building blocks for the design of spintronic devices. Moreover, molecular materials enable the combination of bottom-up processing techniques, for example with conventional top-down nanofabrication. The development of solid-state spintronic devices based on the giant magnetoresistance, tunnel magnetoresistance and spin-valve effects has revolutionized magnetic memory applications. Recently, a significant improvement of the spin-relaxation time has been observed in organic semiconductor tunnel junctions, single non-magnetic molecules coupled to magnetic electrodes have shown giant magnetoresistance and hybrid devices exploiting the quantum tunnelling properties of single-molecule magnets have been proposed. Herein, we present an original spin-valve device in which a non-magnetic molecular quantum dot, made of a single-walled carbon nanotube contacted with non-magnetic electrodes, is laterally coupled through supramolecular interactions to TbPc(2) single-molecule magnets (Pc=phthalocyanine). Their localized magnetic moments lead to a magnetic field dependence of the electrical transport through the single-walled carbon nanotube, resulting in magnetoresistance ratios up to 300% at temperatures less than 1 K. We thus demonstrate the functionality of a supramolecular spin valve without magnetic leads. Our results open up prospects of new spintronic devices with quantum properties.