Random bin-picking is a prominent, useful, and challenging industrial robotics application. However, many industrial and real-world objects are planar and have oriented surface points that are not sufficiently compact and discriminative for those methods using geometry information, especially depth discontinuities. This study solves the above-mentioned problems by proposing a novel and robust solution for random bin-picking for planar objects in a cluttered environment. Different from other research that has mainly focused on 3D information, this study first applies an instance segmentation-based deep learning approach using 2D image data for classifying and localizing the target object while generating a mask for each instance. The presented approach, moreover, serves as a pioneering method to extract 3D point cloud data based on 2D pixel values for building the appropriate coordinate system on the planar object plane. The experimental results showed that the proposed method reached an accuracy rate of 100% for classifying two-sided objects in the unseen dataset, and 3D appropriate pose prediction was highly effective, with average translation and rotation errors less than 0.23 cm and 2.26°, respectively. Finally, the system success rate for picking up objects was over 99% at an average processing time of 0.9 s per step, fast enough for continuous robotic operation without interruption. This showed a promising higher successful pickup rate compared to previous approaches to random bin-picking problems. Successful implementation of the proposed approach for USB packs provides a solid basis for other planar objects in a cluttered environment. With remarkable precision and efficiency, this study shows significant commercialization potential.