A method is presented for high-precision chemical detection that integrates quantum sensing with droplet microfluidics. Using nanodiamonds (ND) with fluorescent nitrogen-vacancy (NV) centers as quantum sensors, rapidly flowing microdroplets containing analyte molecules are analyzed. A noise-suppressed mode of optically detected magnetic resonance is enabled by pairing controllable flow with microwave control of NV electronic spins, to detect analyte-induced signals of a few hundredths of a percent of the ND fluorescence. Using this method, paramagnetic ions in droplets are detected with low limit-of-detection using small analyte volumes, with exceptional measurement stability over >103 s. In addition, these droplets are used as microconfinement chambers by co-encapsulating ND quantum sensors with various analytes such as single cells, suggesting wide-ranging applications including single-cell metabolomics and real-time intracellular measurements from bioreactors. Important advances are enabled by this work, including portable chemical testing devices, amplification-free chemical assays, and chemical imaging tools for probing reactions within microenvironments.