Invaluable records of planetary dynamics and evolution can be recovered from the geochemical systematics of single meteorites(1). However, the interpreted ages of the ejected igneous crust of Mars differ by up to four billion years(1-6), a conundrum(7) due in part to the difficulty of using geochemistry alone to distinguish between the ages of formation and the ages of the impact events that launched debris towards Earth. Here we solve the conundrum by combining in situ electron-beam nanostructural analyses and U-Pb (uranium-lead) isotopic measurements of the resistant micromineral baddeleyite (ZrO2) and host igneous minerals in the highly shock-metamorphosed shergottite Northwest Africa 5298 (ref. 8), which is a basaltic Martian meteorite. We establish that the micro-baddeleyite grains pre-date the launch event because they are shocked, cogenetic with host igneous minerals, and preserve primary igneous growth zoning. The grains least affected by shock disturbance, and which are rich in radiogenic Pb, date the basalt crystallization near the Martian surface to 187 +/- 33 million years before present. Primitive, non-radiogenic Pb isotope compositions of the host minerals, common to most shergottites(1-4), do not help us to date the meteorite, instead indicating a magma source region that was fractionated more than four billion years ago(9-12) to form a persistent reservoir so far unique to Mars(1,9). Local impact melting during ejection from Mars less than 22 +/- 2 million years ago caused the growth of unshocked, launch-generated zircon and the partial disturbance of baddeleyite dates. We can thus confirm the presence of ancient, non-convecting mantle beneath young volcanic Mars, place an upper bound on the interplanetary travel time of the ejected Martian crust, and validate a new approach to the geochronology of the inner Solar System.