In this article we establish a new analytic criterion for univalence of typically-real functions. Moreover, we find geometric properties for functions fulfilling the criterion. The new subclass of univalent functions is defined via these geometric properties. This class can be useful for verifying the univalence of potentially extremal polynomials associated to the work of Dmitrishin, Dyakonov and Stokolos [Anal. Math. Phys. 9 (2019), pp. 991–1004] on univalent polynomials and Koebe’s One-Quarter Theorem.