The fourth industrial revolution has introduced a range of digital technologies (DTs) that possess the potential to significantly enhance the operations and competitiveness of heavy-construction firms. Grounded in the Technology–Organization–Environment (TOE) Framework, the Resource-Based View (RBV) and the Diffusion of Innovation Theory (DOI), this study investigates the relationship between the adoption of digital technologies and the competitive edge (CE) of heavy-engineering firms. Specifically, this research seeks to assess how the adoption of DTs impacts four critical competitive-edge metrics: efficient resource management (CE1), real-time monitoring and control (CE2), data-driven decision-making (CE3) and improved collaboration and communication (CE4). A quantitative research approach was employed, using a structured questionnaire distributed to construction professionals in Lagos State, Nigeria. The principal results of the study revealed that firms adopting artificial intelligence (AI), cloud-based technology and the Internet of Things (IoT) exhibited significantly higher competitive-edge metrics compared to their counterparts. Notably, AI and cloud-based technology were found to have a particularly strong association with improved resource management, real-time monitoring, and decision-making processes. A major contribution of this research is the development of a DT-adoption model which can serve as a benchmarking tool for firms to assess their current adoption levels and identify areas for improvement. This model can also guide policymakers and regulators in developing strategies to encourage the integration of digital technologies within the heavy-construction industry. The originality of this study lies in its holistic approach, examining a broad spectrum of digital technologies and their collective impact on enhancing the competitive edge of construction firms.