Knowledge about the intrinsic electronic properties of water is imperative for understanding the behaviour of aqueous solutions that are used throughout biology, chemistry, physics, and industry. The calculation of the electronic band gap of liquids is challenging, because the most accurate ab initio approaches can be applied only to small numbers of atoms, while large numbers of atoms are required for having configurations that are representative of a liquid. Here we show that a high-accuracy value for the electronic band gap of water can be obtained by combining beyond-DFT methods and statistical time-averaging. Liquid water is simulated at 300 K using a plane-wave density functional theory molecular dynamics (PW-DFT-MD) simulation and a van der Waals density functional (optB88-vdW). After applying a self-consistent GW correction the band gap of liquid water at 300 K is calculated as 7.3 eV, in good agreement with recent experimental observations in the literature (6.9 eV). For simulations of phase transformations and chemical reactions in water or aqueous solutions whereby an accurate description of the electronic structure is required, we suggest to use these advanced GW corrections in combination with the statistical analysis of quantum mechanical MD simulations.