Translation quality estimation is a task of growing importance in NLP, due to its potential to reduce post-editing human effort in disruptive ways. However, this potential is currently limited by the relatively low accuracy of existing systems. In this paper, we achieve remarkable improvements by exploiting synergies between the related tasks of word-level quality estimation and automatic post-editing. First, we stack a new, carefully engineered, neural model into a rich feature-based word-level quality estimation system. Then, we use the output of an automatic post-editing system as an extra feature, obtaining striking results on WMT16: a word-level FMULT1 score of 57.47% (an absolute gain of +7.95% over the current state of the art), and a Pearson correlation score of 65.56% for sentence-level HTER prediction (an absolute gain of +13.36%).