We offer a report on the synthesis of low-molecular weight biobased poly(mannitol sebacate) (PMS) and its functionalization with acrylate groups (PMSAc). These synthesized polyesters were blended at a low level (10 wt%) with poly (lactic acid) PLA to prepare aligned fibers by electrospinning, coupled with a rotatory collector. The obtained fibers were extensively studied by Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and wide-angle X-ray diffraction (WAXS), employing synchrotron radiation. The incorporation of the PMSs on the PLA fibers did not significantly affect the fiber diameters, whereas the alignment was almost maintained. The crystallinity and thermal properties were also slightly modified with the addition of PMSs, and an increase in the degree of crystallinity and in the glass transition temperature of the blend compared to PLA was observed. Remarkably, the PLA/PMSs fibers were more ductile due to the elastomeric character of PMS, with higher values of elongation at break and tensile strengths, and a smaller Young modulus in comparison with the PLA fibers. These modifications of the properties were more noticeable in the case of the acrylated PMS, which also provided readily available functional groups at the surface for further chemical reactions, such as the Michael addition or crosslinking processes.