We present a new dynamical study of the black hole X-ray transient GRS1915+105 making use of near-infrared spectroscopy obtained with X-shooter at the VLT. We detect a large number of donor star absorption features across a wide range of wavelengths spanning the H and K bands. Our 24 epochs covering a baseline of over 1 year permit us to determine a new binary ephemeris including a refined orbital period of P=33.85 +/- 0.16 d. The donor star radial velocity curves deliver a significantly improved determination of the donor semi-amplitude which is both accurate (K_2=126 +/- 1 km/s) and robust against choice of donor star template and spectral features used. We furthermore constrain the donor star's rotational broadening to vsini=21 +/-4 km/s, delivering a binary mass ratio of q=0.042 +/- 0.024. If we combine these new constraints with distance and inclination estimates derived from modelling the radio emission, a black hole mass of M_BH=10.1 +/- 0.6 M_sun is inferred, paired with an evolved mass donor of M_2=0.47 +/- 0.27 M_sun. Our analysis suggests a more typical black hole mass for GRS1915+105 rather than the unusually high values derived in the pioneering dynamical study by Greiner et al. (2001). Our data demonstrate that high-resolution infrared spectroscopy of obscured accreting binaries can deliver dynamical mass determinations with a precision on par with optical studies. ; Comment: 7 pages, 5 figures, accepted for publication in the Astrophysical Journal