Rice–wheat cropping system (RWCS) is a dominant agricultural practice in the Indo-Gangetic plains, particularly in the North–Western states of India. The prevalent practice of open burning of rice residue, driven by the need for timely land preparation, poses severe environmental and health consequences, including nutrient loss, greenhouse gas emissions, high concentrations of particulate matter (PM), and disruption of the ecological cycle. This study focuses on implementing effective management practices in the RWCS through tillage-based crop establishment, residue retention, and incorporation methods. The objective is to improve crop yield and its attributes by enhancing soil health properties. A split-plot experimental design was practiced with four different treatments, zero-tillage with manual harvesting (ZT), Happy Seeder with combine harvester (HS), Happy Seeder with Mulcher and combine harvesting, and conventional tillage (CT). By evaluating soil nutrient content, including organic carbon (OC), N, P, and K, at a 0–10 cm depth, the study demonstrates the superiority of the mulcher with Happy Seeder (MHS), which significantly increased soil nutrient levels by 105, 59, 102, and 97%, respectively, compared to conventional tilled broadcasted wheat (CT). Furthermore, the MHS treatment exhibited the highest yield of 56.8 q ha−1, outperforming the yield of 43.6 q ha−1 recorded under conventional tilled broadcasted wheat. These findings underscore the critical role of surface residue retention with MHS in ensuring crop productivity and overall production sustainability of the RWCS in Haryana, India. Moreover, effective rice residue management holds long-term implications for agricultural resilience, farm economics, environmental conservation, and human health. It emphasizes the importance of adopting sustainable practices, prioritizing research efforts, and advocating for policies that ensure the prolonged sustainability and productivity of the RWCS while safeguarding environmental well-being.