We establish a group-action version of the Szemerédi-Trotter theorem over any field, extending Bourgain's result for the group $\mathrm{SL}_2(k)$. As an Elekes-Szabó-type application, we obtain quantitative bounds on the number of collinear triples on reducible cubic surfaces in $\mathbb{P}^3(k)$, where $k = \mathbb{F}_{q}$ and $k = \mathbb{C}$, thereby improving a recent result by Bays, Dobrowolski, and the second author.