In this paper, we analytically compute all master integrals for one of the two non-planar integral families for five-particle massless scattering at two loops. We first derive an integral basis of 73 integrals with constant leading singularities. We then construct the system of differential equations satisfied by them, and find that it is in canonical form. The solution space is in agreement with a recent conjecture for the non-planar pentagon alphabet. We fix the boundary constants of the differential equations by exploiting constraints from the absence of unphysical singularities. The solution of the differential equations in the Euclidean region is expressed in terms of iterated integrals. We cross-check the latter against previously known results in the literature, as well as with independent Mellin-Barnes calculations.