First-order phase transitions in solids are notoriously challenging to study. The combination of change in unit cell shape, long range of elastic distortion and flow of latent heat leads to large energy barriers resulting in domain structure, hysteresis and cracking. The situation is worse near a triple point, where more than two phases are involved. The well-known metal-insulator transition in vanadium dioxide, a popular candidate for ultrafast optical and electrical switching applications, is a case in point. Even though VO2 is one of the simplest strongly correlated materials, experimental difficulties posed by the first-order nature of the metal-insulator transition as well as the involvement of at least two competing insulating phases have led to persistent controversy about its nature. Here we show that studying single-crystal VO2 nanobeams in a purpose-built nanomechanical strain apparatus allows investigation of this prototypical phase transition with unprecedented control and precision. Our results include the striking finding that the triple point of the metallic phase and two insulating phases is at the transition temperature, Ttr = Tc, which we determine to be 65.0 ± 0.1 °C. The findings have profound implications for the mechanism of the metal-insulator transition in VO2, but they also demonstrate the importance of this approach for mastering phase transitions in many other strongly correlated materials, such as manganites and iron-based superconductors.