Warming‐driven expansion of the oxygen minimum zone (OMZ) in the equatorial Pacific would bring very low oxygen waters closer to the ocean surface and possibly impact global carbon/nutrient cycles and local ecosystems. Global coarse Earth System Models (ESMs) show, however, disparate trends that poorly constrain these future changes in the upper OMZ. Using an ESM with a high‐resolution ocean (1/10°), we show that a realistic representation of the Equatorial Undercurrent (EUC) dynamics is crucial to represent the upper OMZ structure and its temporal variability. We demonstrate that coarser ESMs commonly misrepresent the EUC, leading to an unrealistic “tilt” of the OMZ (e.g., shallowing toward the east) and an exaggerated sensitivity to EUC changes overwhelming other important processes like diffusion and biology. This shortcoming compromises the ability to reproduce the OMZ variability and could explain the disparate trends in ESMs projections.