Autonomous micro aerial vehicles still struggle with fast and agile maneuvers, dynamic environments, imperfect sensing, and state estimation drift. Autonomous drone racing brings these challenges to the fore. Human pilots can fly a previously unseen track after a handful of practice runs. In contrast, state-of-the-art autonomous navigation algorithms require either a precise metric map of the environment or a large amount of training data collected in the track of interest. To bridge this gap, we propose an approach that can fly a new track in a previously unseen environment without a precise map or expensive data collection. Our approach represents the global track layout with coarse gate locations, which can be easily estimated from a single demonstration flight. At test time, a convolutional network predicts the poses of the closest gates along with their uncertainty. These predictions are incorporated by an extended Kalman filter to maintain optimal maximum-aposteriori estimates of gate locations. This allows the framework to cope with misleading high-variance estimates that could stem from poor observability or lack of visible gates. Given the estimated gate poses, we use model predictive control to quickly and accurately navigate through the track. We conduct extensive experiments in the physical world, demonstrating agile and robust flight through complex and diverse previouslyunseen race tracks. The presented approach was used to win the IROS 2018 Autonomous Drone Race Competition, outracing the second-placing team by a factor of two.