Autonomous drone racing represents a major frontier in robotics research. It requires an Artificial Intelligence (AI) that can run on board light-weight flying robots under tight resource and time constraints, while pushing the physical system to its limits. The state of the art in this area consists of a system with a stereo camera and an inertial measurement unit (IMU) that beat human drone racing champions in a controlled indoor environment. Here, we present MonoRace: an onboard drone racing approach that uses a monocular, rolling-shutter camera and IMU that generalizes to a competition environment without any external motion tracking system. The approach features robust state estimation that combines neural-network-based gate segmentation with a drone model. Moreover, it includes an offline optimization procedure that leverages the known geometry of gates to refine any state estimation parameter. This offline optimization is based purely on onboard flight data and is important for fine-tuning the vital external camera calibration parameters. Furthermore, the guidance and control are performed by a neural network that foregoes inner loop controllers by directly sending motor commands. This small network runs on the flight controller at 500Hz. The proposed approach won the 2025 Abu Dhabi Autonomous Drone Racing Competition (A2RL), outperforming all competing AI teams and three human world champion pilots in a direct knockout tournament. It set a new milestone in autonomous drone racing research, reaching speeds up to 100 km/h on the competition track and successfully coping with problems such as camera interference and IMU saturation.