Phishing attacks pose a significant and escalating threat to cybersecurity in recent times. This deceptive scam aims to trick naive users, luring them into visiting harmful websites and sharing sensitive information, including credentials, credit card numbers, and passwords. Consequently, cybercriminals exploit this data for their own gain. As the sophistication and maliciousness of phishing continue to evolve, researchers are earnestly developing multiple anti-phishing solutions in the literature. Among these solutions, those based on deep learning models have gained substantial attention in recent years. This study proposes an intelligent, deep-learning-based mechanism to detect phishing URLs. The proposed system is based on the permutation importance method (PIM) to select the most relevant URL features, and the Smote-Tomek link method to solve the problem of an unbalanced dataset. In addition, four DL models—CNN, LSTM, and two hybrid models (CNN-LSTM and LSTM-CNN)—are tested to identify the more suitable detection model for the phishing field. The experimental results demonstrate the successful functioning of the proposed phishing detection mechanism. It is observed that the proposed mechanism achieved an accuracy ranging from 93.36% to 96.43% without feature selection and data balance across two variants of datasets and different DL classifiers. It also achieved an accuracy ranging from 94.12% to 96.88% with feature selection and data balance. Finally, our phishing detection mechanism is implemented as web application to enhance its usability for web users.