A diagnostic system for a vehicle includes an error module, an equivalence ratio (EQR) module, a threshold determination module, and a fault indication module. The error module determines an error value based on a difference between an amount of oxygen in exhaust measured by an exhaust gas oxygen sensor (EGO) upstream of a catalyst and an expected value of the amount. The EQR module selectively controls fuel injection based on the error value. The threshold determination module determines an error threshold based on a flow rate of fuel vapor from a vapor canister to an intake manifold of an engine. The fault indication module selectively indicates that a fault is present in the EGO sensor based on the error value and the error threshold.