Accurate estimation of interaction forces is crucial for achieving fine, dexterous control in robotic systems. Although tactile sensor arrays offer rich sensing capabilities, their effective use has been limited by challenges such as calibration complexities, nonlinearities, and deformation. In this paper, we tackle these issues by presenting a novel method for obtaining 3D force estimation using tactile sensor arrays. Unlike existing approaches that focus on specific or decoupled force components, our method estimates full 3D interaction forces across an array of distributed sensors, providing comprehensive real-time feedback. Through systematic data collection and model training, our approach overcomes the limitations of prior methods, achieving accurate and reliable tactile-based force estimation. Besides, we integrate this estimation in a real-time control loop, enabling implicit, stable force regulation that is critical for precise robotic manipulation. Experimental validation on the Allegro robot hand with uSkin sensors demonstrates the effectiveness of our approach in real-time control, and its ability to enhance the robot's adaptability and dexterity.