[en] Matrix integrals used in random matrix theory have been revealed to provide τ-functions for several hierarchies of soliton equations. In this article, we extend this relation by showing that such integrals can also provide τ-functions for the q-difference two-dimensional Toda lattice (q-2DTL) equation and its Pfaffianized system obtained by Pfaffianization. We consider a particular form of matrix integrals, which we show gives determinant solutions and Pfaffian solutions to the q-2DTL equation and its Pfaffianized system in different cases, respectively. (author)