Can language analysis reveal the underlying social power relations that exist between participants of an interaction? Prior work within NLP has shown promise in this area, but the performance of automatically predicting power relations using NLP analysis of social interactions remains wanting. In this paper, we present a novel neural architecture that captures manifestations of power within individual emails which are then aggregated in an order-preserving way in order to infer the direction of power between pairs of participants in an email thread. We obtain an accuracy of 80.4%, a 10.1% improvement over state-of-the-art methods, in this task. We further apply our model to the task of predicting power relations between individuals based on the entire set of messages exchanged between them; here also, our model significantly outperforms the 70.0% accuracy using prior state-of-the-art techniques, obtaining an accuracy of 83.0%.