Overtaking on two-lane roads is a great challenge for autonomous vehicles, as oncoming traffic appearing on the opposite lane may require the vehicle to change its decision and abort the overtaking. Deep reinforcement learning (DRL) has shown promise for difficult decision problems such as this, but it requires massive number of data, especially if the action space is continuous. This paper proposes to incorporate guidance from an expert system into DRL to increase its sample efficiency in the autonomous overtaking setting. The guidance system developed in this study is composed of constrained iterative LQR and PID controllers. The novelty lies in the incorporation of a fading guidance function, which gradually decreases the effect of the expert system, allowing the agent to initially learn an appropriate action swiftly and then improve beyond the performance of the expert system. This approach thus combines the strengths of traditional control engineering with the flexibility of learning systems, expanding the capabilities of the autonomous system. The proposed methodology for autonomous vehicle overtaking does not depend on a particular DRL algorithm and three state-of-the-art algorithms are used as baselines for evaluation. Simulation results show that incorporating expert system guidance improves state-of-the-art DRL algorithms greatly in both sample efficiency and driving safety.