  We show that if the moment-angle complex $\mathcal{Z}_K$ associated to a
simplicial complex $K$ is homotopy equivalent to a connected sum of sphere
products with two spheres in each product, then $K$ decomposes as the
simplicial join of an $n$-simplex $\Delta^n$ and a minimally non-Golod complex.
In particular, we prove that $K$ is minimally non-Golod for every moment-angle
complex $\mathcal{Z}_K$ homeomorphic to a connected sum of two-fold products of
spheres, answering a question of Grbi\'c, Panov, Theriault and Wu.
