We propose a new framework for object detection that guides the model to explicitly reason about translation and rotation invariant object keypoints to boost model robustness. The model first predicts keypoints for each object in the image and then derives bounding-box predictions from the keypoints. While object classification and box regression are supervised, keypoints are learned through self-supervision by comparing keypoints predicted for each image with those for its affine transformations. Thus, the framework does not require additional annotations and can be trained on standard object detection datasets. The proposed model is designed to be anchor-free, proposal-free, and single-stage in order to avoid associated computational overhead and hyperparameter tuning. Furthermore, the generated keypoints allow for inferring close-fit rotated bounding boxes and coarse segmentation for free. We propose to evaluate our model on the standard PASCAL VOC and MS COCO datasets and metrics along with new specialized experiments designed for assessing robustness to translation and rotation. Finally, the segmentation utility of generated keypoints would be evaluated on the MS COCO dataset.