The cultivation of tiger nut (Cyperus esculentus L.) on marginal lands is a feasible and effective way to increase food production in Northern China. However, the specific influence of nitrogen fertilizer application on the growth dynamics, tuber expansion, overall yield, and nitrogen use efficiency (NUE) of tiger nuts cultivated on these sandy lands is yet to be fully elucidated. From 2021 to 2022, we conducted a study to determine the effect of N fertilizers on the leaf function morphology, canopy apparent photosynthesis (CAP), tuber yield, and NUE of tiger nut. The results indicate that the tuber yield and NUE are closely related to the specific leaf area (SLA), leaf area index (LAI), leaf nitrogen concentration per area (NA), CAP, and tuber expansion characteristics. Notably, significant enhancements in the SLA, LAI, NA, and CAP during the tuber expansion phase ranging from the 15th to the 45th day under the 300 kg N ha−1 treatment were observed, subsequently leading to increases in both the tuber yield and NUE. Moreover, a maximum average tuber filling rate was obtained under the N300 treatment. These improvements led to substantial increases in the tuber yield (32.1–35.5%), nitrogen agronomic efficiency (NAE, 2.1–5.3%), nitrogen partial factor productivity (NPP, 4.8–8.1%), and nitrogen recovery efficiency (NRE, 3.4–5.7%). Consequently, 300 kg N ha−1 of N fertilizers is the most effective dose for optimizing both the yield of tiger nut tubers and the NUE of tiger nut plants in marginal soils. Structural equation modeling reveals that N application affects the yield and NUE through its effects on leaf functional traits, the CAP, and the tuber filling characteristics. Modeling indicates that tuber expansion characteristics primarily impact the yield, while CAP predominantly governs the NUE. Above all, this study highlights the crucial role of N fertilizer in maximizing the tiger nut tuber yield potential on marginal lands, providing valuable insights into sustainable farming in dry areas.