Noise is a fundamental challenge for sensors deployed in daily environments for ambient sensing, health monitoring, and wireless networking. Current strategies for noise mitigation rely primarily on reducing or removing noise. Here, we introduce stochastic exceptional points and show the utility to reverse the detrimental effect of noise. The stochastic process theory illustrates that the stochastic exceptional points manifest as fluctuating sensory thresholds that give rise to stochastic resonance, a counterintuitive phenomenon in which the added noise increases the system's ability to detect weak signals. Demonstrations using a wearable wireless sensor show that the stochastic exceptional points lead to more accurate tracking of a person's vital signs during exercise. Our results may lead to a distinct class of sensors that overcome and are enhanced by ambient noise for applications ranging from healthcare to the internet of things.