Reagents can be pulled through an endergonic reaction, if the reaction products are cleared rapidly by a subsequent exergonic reaction.  The concentration of the products of the endergonic reaction thus always remains low, so the reaction can proceed.
A classic example of this might be the first stage of a reaction which proceeds via a transition state.  The process of getting to the top of the activation energy barrier to the transition state is endergonic.  However, the reaction can proceed because having reached the transition state, it rapidly evolves via an exergonic process to the more stable final products.