The debate about the universality of the stellar initial mass function (IMF) revolves around two competing lines of evidence. While measurements in the Milky Way, an archetypal spiral galaxy, seem to support an invariant IMF, the observed properties of massive early-type galaxies (ETGs) favor an IMF somehow sensitive to the local star-formation conditions. However, the fundamental methodological and physical differences between the two approaches have hampered a comprehensive understanding of IMF variations. Here, we describe an improved modeling scheme that, for the first time, allows consistent IMF measurements across stellar populations with different ages and complex star-formation histories (SFHs). Making use of the exquisite MUSE optical data from the TIMER survey and powered by the MILES stellar population models, we show the age, metallicity, [Mg/Fe], and IMF slope maps of the inner regions of NGC 3351, a spiral galaxy with a mass similar to that of the Milky Way. The measured IMF values in NGC 3351 follow the expectations from a Milky Way-like IMF, although they simultaneously show systematic and spatially coherent variations, particularly for low-mass stars. In addition, our stellar population analysis reveals the presence of metal-poor and Mg-enhanced star-forming regions that appear to be predominantly enriched by the stellar ejecta of core-collapse supernovae. Our findings therefore showcase the potential of detailed studies of young stellar populations to provide the means to better understand the early stages of galaxy evolution and, in particular, the origin of the observed IMF variations beyond and within the Milky Way.