Cultivating multiple crops together can provide numerous benefits, including improved soil health and crop yield. The objective of our study was to determine the optimum planting techniques in intercropping systems, and to maximize their benefits by mitigating competition for resources such as land, space, light interception, and nutrition. The performance of successively planted maize (Zea mays L.) grown with cowpea (Vigna unguiculata L.) was evaluated with a field trial in Bangladesh. The treatments in our study were: (a) sole maize, (b) sole cowpea, (c) crops sown simultaneously, and (d) crops sown with different time lags (1, 2, and 3 weeks) between the maize-sowing and cowpea-sowing dates. Data on the crops’ physiological parameters were recorded. These included light interception, leaf area index (LAI), Soil Plant Analysis Development (SPAD), harvest index, and yield. Simultaneously, canopy coverage was measured using camera-based photo analysis. In addition, an economic analysis of intercropping maize with soybean or cowpea was conducted using gross margin analysis and benefit-cost ratio. In our results, the below-canopy photosynthetically active radiation (PAR) was significantly higher in intercropping treatments when maize was sown three weeks after cowpea. In contrast, the LAI value of the maize and cowpea was significantly greater when sown on the same day than in other intercropping treatments. As a result, the maize yield reduced when intercropped with cowpea. This reduction maximized when both species were sown simultaneously due to higher competition for resources, including nutrients and light. Intercropping was more beneficial in terms of land equivalent ratio than both sole cropping of maize and cowpea, especially when maize was planted three weeks later. However, this benefit was not retained when calculated as maize equivalent yield since the contribution of cowpea was small in the overall maize yield, suggesting the importance of the relative economic value of the component species. Among all treatments, the lowest maize equivalent yield (6.03 ± 0.14 t ha−1) was obtained from sole cowpea, and the largest land equivalent ratio (1.67 ± 0.05) was obtained from intercropping with maize sown three weeks after cowpea. This treatment provided a net income of USD 786.32 ± 25.08 ha−1. This study has shown that together, maize–cowpea intercropping with a temporal niche difference of three weeks may be a better option for sustainable crop production in Bangladesh, maximizing land use. However, it may not provide a significantly greater maize equivalent yield and economic return.