Cybercriminals use domain generation algorithms (DGAs) to prevent their servers from being potentially blacklisted or shut down. Existing reverse engineering techniques for DGA detection is labor intensive, extremely time-consuming, prone to human errors, and have significant limitations. Hence, an automated real-time technique with a high detection rate is warranted in such applications. In this article, we present a novel technique to detect randomly generated domain names and domain name system (DNS) homograph attacks without the need for any reverse engineering or using nonexistent domain (NXDomain) inspection using deep learning. We provide an extensive evaluation of our model over four large, real-world, publicly available datasets. We further investigate the robustness of our model against three different adversarial attacks: DeepDGA, CharBot, and MaskDGA. Our evaluation demonstrates that our method is effectively able to identify DNS homograph attacks and DGAs and also is resilient to common evading cyberattacks. Promising results show that our approach provides a more effective detection rate with an accuracy of 0.99. Additionally, the performance of our model is compared against the most popular deep learning architectures. Our findings highlight the essential need for more robust detection models to counter adversarial learning.