Robotic automation has the potential to assist human surgeons in performing suturing tasks in microsurgery, and in order to do so a robot must be able to guide a needle with sub-millimeter precision through soft tissue. This paper presents a robotic suturing system that uses 3D optical coherence tomography (OCT) system for imaging feedback. Calibration of the robot-OCT and robot-needle transforms, wound detection, keypoint identification, and path planning are all performed automatically. The calibration method handles pose uncertainty when the needle is grasped using a variant of iterative closest points. The path planner uses the identified wound shape to calculate needle entry and exit points to yield an evenly-matched wound shape after closure. Experiments on tissue phantoms and animal tissue demonstrate that the system can pass a suture needle through wounds with 0.200 mm overall accuracy in achieving the planned entry and exit points, and over 20× more precise than prior autonomous suturing robots.