Recent studies have revealed that global extrinsic noise arising from stochasticity in the intracellular biochemical environment plays a critical role in heterogeneous cell physiologies. However, it remains largely unclear how such extrinsic noise dynamically influences downstream reactions and whether it could be neutralized by cellular reactions. Here, using fluorescent protein (FP) maturation as a model biochemical reaction, we explored how cellular reactions might combat global extrinsic noise in mammalian cells. We developed a novel single-cell assay to systematically quantify the maturation rate and the associated noise for over a dozen FPs. By exploiting the variation in the maturation rate for different FPs, we inferred that global extrinsic noise could be temporally filtered by maturation reactions, and as a result, the noise levels for slow-maturing FPs are lower compared to fast-maturing FPs. This mechanism is validated by directly perturbing the maturation rates of specific FPs and measuring the resulting noise levels. Together, our results revealed a potentially general principle governing extrinsic noise propagation, where timescale separation allows cellular reactions to cope with dynamic global extrinsic noise.