Quantum devices for sensing and computing applications require coherent quantum systems, which can be manipulated in fast and robust ways1. Such quantum control is typically achieved using external electromagnetic fields, which drive the system’s orbital2, charge3 or spin4,5 degrees of freedom. However, most existing approaches require complex and unwieldy gate structures, and with few exceptions6,7 are limited to the regime of weak coherent driving. Here, we present a novel approach to coherently drive a single electronic spin using internal strain fields8,9,10 in an integrated quantum device. Specifically, we employ time-varying strain in a diamond cantilever to induce long-lasting, coherent oscillations of an embedded nitrogen–vacancy (NV) centre spin. We perform direct spectroscopy of the phonon-dressed states emerging from this drive and observe hallmarks of the sought-after strong-driving regime6,11, where the spin rotation frequency exceeds the spin splitting. Furthermore, we employ our continuous strain driving to significantly enhance the NV’s spin coherence time12. Our room-temperature experiments thereby constitute an important step towards strain-driven, integrated quantum devices and open new perspectives to investigate unexplored regimes of strongly driven multilevel systems13 and exotic spin dynamics in hybrid spin-oscillator devices14.