ABSTRACT We measure the galaxy two- and three-point correlation functions at z = [0.5, 0.7] and z = [0.7, 0.9], from the Public Data Release 2 (PDR2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS). We model the two statistics including a non-linear one-loop model for the two-point function and a tree-level model for the three-point function, and perform a joint likelihood analysis. The entire process and non-linear corrections are tested and validated through the use of the 153 highly realistic VIPERS mock catalogues, showing that they are robust down to scales as small as 10 $h^{-1} \, \mathrm{Mpc}$. The mocks are also adopted to compute the covariance matrix that we use for the joint two- and three-point analysis. Despite the limited statistics of the two (volume-limited) subsamples analysed, we demonstrate that such a combination successfully breaks the degeneracy existing at two-point level between clustering amplitude σ8, linear bias b1, and the linear growth rate of fluctuations f. For the latter, in particular, we measure $f(z=0.61)=0.64^{+0.55}_{-0.37}$ and f(z = 0.8) = 1.0 ± 1.0, while the amplitude of clustering is found to be σ8(z = 0.61) = 0.50 ± 0.12 and $\sigma _8(z=0.8)=0.39^{+0.11}_{-0.13}$. These values are in excellent agreement with the extrapolation of a Planck cosmology.