One-stage object detectors rely on a point feature to predict the detection results. However, the point feature often lacks the information of the whole object, thereby leading to a misalignment between the object and the point feature. Meanwhile, the classification and regression tasks are sensitive to different object regions, but their features are spatially aligned. Both of these two problems hinder the detection performance. In order to solve these two problems, we propose a simple and plug-in operator that can generate aligned and disentangled features for each task, respectively, without breaking the fully convolutional manner. By predicting two task-aware point sets that are located in each sensitive region, the proposed operator can align the point feature with the object and disentangle the two tasks from the spatial dimension. We also reveal an interesting finding of the opposite effect of the long-range skip connection for classification and regression. On the basis of the Object-Aligned and Task-disentangled operator (OAT), we propose OAT-Net, which explicitly exploits point-set features for accurate detection results. Extensive experiments on the MS-COCO dataset show that OAT can consistently boost different state-of-the-art one-stage detectors by $\sim$2 AP. Notably, OAT-Net with Res2Net-101-DCN backbone achieves 53.7 AP on the COCO test-dev.