In this paper we present a balanced truncation based strategy for the numerical solution of optimal control problems governed by nonlinear evolution partial differential equations. The idea consists in utilizing a balanced truncation model reduction method for the efficient solution of the semidiscretized adjoint system, while the nonlinear state equations are fully solved. Our strategy is analyzed as a descent method in function spaces and global convergence results are presented. In combination with a Broyden-Fletcher-Goldfarb-Shanno update also superlinear convergence is verified. Numerical examples are given to illustrate the behaviour of the proposed method for different problems.