As new lightweight hardware security primitive, the physical unclonable function (PUF) is used in various hardware-based secure applications like keys generation and device authentication. But PUFs are vulnerable to modeling attacks using machine learning (ML) technology. To solve the problem, a dynamically configurable obfuscation unit for PUF using a dynamic linear feedback shift register (DLFSR) is proposed. The structure of this obfuscation unit can change with the clock cycle running, making the PUF difficult to model. Using the obfuscation unit, a dual-PUF-based mutual device authentication protocol for low-cost IoT systems is proposed. New technologies like dual-stage and device-to-server authentication are used to limit the amount of data that an attacker can obtain. A random pattern-based mechanism is introduced to the protocol to enhance the robustness against physical attacks. A mathematical model of the proposed unit is presented and analyzed. Experimental results on FPGA show that the design is simpler, more reliable, and lightweight. It can effectively resist ML-based attacks and physical attacks.