The rapid expansion of the Internet of Things (IoT) creates a modern infrastructure that is challenging for robust security. Vulnerability is an important issue for connected devices against various intrusion attacks. The existing systems face some challenges when considering Deep Learning (DL) methods, which include computational cost, real-time detection, and unseen threats generalization. To overcome these problems, in this paper proposes a Hybrid Intrusion Detection System for IoT (HYDEST-IoT) that can detect the cyber threats efficiently. The system is built on top of a Sparse Autoencoder (SAE) for feature extraction and Bidirectional Gated Recurrent Unit (BiGRU) for precise temporal pattern classification. The objective of this work is to provide a robust and efficient Intrusion Detection System (IDS) for resource-limited IoT deployments. This study was implemented using Python and it was trained and tested through the NSL-KDD dataset. This provided a comparison of HYDEST-IoT with existing methods including A-BiLSTM, SAE-CNN, and DCGR_IoT. The proposed HYDEST-IoT reached 99.7% accuracy, a lower False Alarm Rate (FAR) and less computational time of 4s, in which it gets both efficiency and detection performance. HYDEST-IoT was a small framework that could be used for such resource starved IoT environment.