Magnetic tunnel junctions (MTJs) based on ferromagnets are canonical devices in spintronics, with wide-ranging applications in data storage, computing, and sensing. They simultaneously exhibit mechanisms for electrical detection and control of magnetic order through the tunneling magnetoresistance (TMR) and spin-transfer torque (STT) effects, respectively. It was long assumed that neither of these effects could be sizeable in all-antiferromagnetic tunnel junctions (AATJs), since they exhibit no net magnetization. Recently, however, it was shown that AATJs based on chiral antiferromagnets do exhibit TMR due to their non-relativistic momentum-dependent spin polarization and cluster magnetic octupole moment (CMO), which are manifestations of their spin-split band structure. However, the reciprocal effect, i.e., the antiferromagnetic counterpart of STT, has been assumed non-existent due to the total electric current being spin-neutral. Here, we report nanoscale AATJs exhibiting this reciprocal effect, which we term octupole-driven spin-transfer torque (OTT). We demonstrate current-induced OTT switching of PtMn3|MgO|PtMn3 AATJs, exhibiting a TMR value of 363% at room temperature and switching current densities of the order of 10 MA/cm2. Our theoretical modeling explains the origin of OTT in terms of the imbalance between intra- and inter-sublattice spin currents across the AATJ, and equivalently, in terms of the non-zero net cluster octupole polarization of each PtMn3 layer. This work establishes a new materials platform for antiferromagnetic spintronics and provides a pathway towards deeply scaled magnetic memory and room-temperature terahertz technologies.