The majority of cataclysmic variable (CV) stars contain a stochastic noise component in their light curves, commonly referred to as flickering. This can significantly affect the morphology of CV eclipses and increases the difficulty in obtaining accurate system parameters with reliable errors through eclipse modelling. Here we introduce a new approach to eclipse modelling, which models CV flickering with the help of Gaussian processes (GPs). A parametrized eclipse model - with an additional GP component - is simultaneously fitted to eight eclipses of the dwarf nova ASASSN-14ag and system parameters determined. We obtain a mass ratio q = 0.149 ± 0.016 and inclination i = 83.4°^{+0.9°}_{-0.6°}. The white dwarf and donor masses were found to be Mw = 0.63 ± 0.04 M⊙ and Md = 0.093 ^{+0.015}_{-0.012} M⊙, respectively. A white dwarf temperature Tw = 14 000 ^{+2200}_{-2000} K and distance d = 146 ^{+24}_{-20} pc were determined through multicolour photometry. We find GPs to be an effective way of modelling flickering in CV light curves and plan to use this new eclipse modelling approach going forward.