On-chip networks are especially vulnerable to within-die parameter variations. Since they connect distant parts of the chip, they need to be designed to work under the most unfavorable parameter values in the chip. This results in energy-inefficient designs. To improve the energy efficiency of on-chip networks, this paper presents a novel approach that relies on monitoring the errors of messages as they traverse the network. Based on the observed errors of messages, the system dynamically decreases or increases the voltage (Vdd) of groups of network routers. With this approach, called Tangle, the different Vdd values applied to different groups of network routers progressively converge to their lowest, variation-aware, error-free values - always keeping the network frequency unchanged. This saves substantial network energy. In a simulated 64-router network with 4 V dd domains, Tangle reduces the network energy consumption by an average of 22% with negligible performance impact. In a future network design with one Vdd domain per router, Tangle lowers the network V dd by an average of 21%, reducing the network energy consumption by an average of 28% with negligible performance impact.