Since its first observation in 2005, the vector charmonium Y(4260) has turned out to be one of the prime candidates for an exotic state in the charmonium spectrum. It was recently proposed that the Y(4260) should have a prominent D-1(D) over bar + c.c molecular component that is strongly correlated with the production of the charged Z(c)(3900). In this paper we demonstrate that the nontrivial cross section line shapes of e(+)e(-) --> J/Psi pi pi and h(c)pi pi can be naturally explained by the molecular scenario. As a consequence we find a significantly smaller mass for the Y(4260) than previously studied. In the e(+)e(-) --> (D) over barD*pi + c.c. process, with the inclusion of an additional S-wave (D) over bar*pi contribution constrained from data on the D (D) over bar* invariant mass distribution, we obtain a good agreement with the data of the angular distributions. We also predict an unusual line shape of Y(4260) in this channel that may serve as a smoking gun for a predominantly molecular nature of Y(4260). Improved measurements of these observables are therefore crucial for a better understanding of the structure of this famous resonance.