Computational gene-function prediction generates annotations at a scale that experimental characterization cannot match, yet substantial errors remain even among leading methods. Explicit error-controlled calibration for Gene Ontology (GO) prediction remains largely undeveloped. We introduce GoCo, a structure-guided framework that calibrates how scores from an existing predictor are converted into released annotations. GoCo certifies a global threshold for a GO-hierarchy-aware gene-level false discovery proportion (FDP), then constructs a nested release path under the same asymptotic risk-control guarantee. At the primary operating point (alpha=0.10, delta=0.50), GoCo-M, developed on Wainberg co-essentiality modules and applied without retuning to three independent studies with the same shared-evidence structure, kept mean held-out gene-level FDP at or below target while releasing 6.3-17.6% more reference-supported GO terms than Multilabel. For gene-specific neighbourhoods, GoCo-N orders individual calls. Developed on FunMap and validated without retuning on the STRING v12.0 experiments-only network, GoCo-N released 33.8% and 36.4% more reference-supported GO terms than Multilabel on the same refined score grid in FunMap and STRING, respectively, while keeping mean held-out FDP below target. The same pattern held under the stricter delta=0.10 setting. Thus, predictor-native biological structure can be reused at calibration, not only prediction, to release more supported annotations at a chosen gene-level error target without retraining the predictor.

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