The free expansion of a planar plasma surface is a fundamental non-equilibrium process relevant for various fields but as-yet experimentally still difficult to capture. The significance of the associated spatiotemporal plasma motion ranges from astrophysics and controlled fusion to laser machining, surface high-harmonic generation, plasma mirrors, and laser-driven particle acceleration. Here, we show that x-ray coherent diffractive imaging can surpass existing approaches and enables the quantitative real-time analysis of the sudden free expansion of laser-heated nanoplasmas. For laser-ionized SiO2 nanospheres, we resolve the formation of the emerging nearly self-similar plasma profile evolution and expose the so far inaccessible shell-wise expansion dynamics including the associated startup delay and rarefaction front velocity. Our results establish time-resolved diffractive imaging as an accurate quantitative diagnostic platform for tracing and characterizing plasma expansion and indicate the possibility to resolve various laser-driven processes including shock formation and wave-breaking phenomena with unprecedented resolution.