In this paper we propose a superadiabatic protocol where quantum state transfer can be achieved with arbitrarily high accuracy and minimal control across long spin chains with an odd number of spins. The quantum state transfer protocol only requires the control of the couplings between the qubits on the edge and the spin chain. We predict fidelities above 0.99 for an evolution of nanoseconds using typical spin-exchange coupling values of μeV. Furthermore, by building a superadiabatic formalism on top of this protocol, we propose an effective superadiabatic protocol that retains the minimal control over the spin chain and further improves the fidelity.