We present a novel method that breaks the resolution barrier in nuclear magnetic resonance (NMR) spectroscopy, allowing one to accurately estimate the chemical shift values of highly overlapping or broadened peaks. This problem is routinely encountered in NMR when peaks have large linewidths due to rapidly decaying signals, hindering its application. We address this problem based on the notion of finite-rate-of-innovation (FRI) sampling, which is based on the premise that signals such as the NMR signal, can be accurately reconstructed using fewer measurements than that required by existing approaches. The FRI approach leads to super-resolution, beyond the limits of contemporary NMR techniques. Using this method, we could measure for the first time small changes in chemical shifts during the formation of a Gold nanorod-protein complex, facilitating the quantification of the strength of such interactions. The method thus opens up new possibilities for the application and acceleration of multidimensional NMR spectroscopy across a wide range of systems.