Systems for time sequential capture of microliter volumes of sweat released from targeted regions of the skin offer the potential to enable analysis of temporal variations in electrolyte balance and biomarker concentration throughout a period of interest. Current methods that rely on absorbent pads taped to the skin do not offer the ease of use in sweat capture needed for quantitative tracking; emerging classes of electronic wearable sweat analysis systems do not directly manage sweat‐induced fluid flows for sample isolation. Here, a thin, soft, “skin‐like” microfluidic platform is introduced that bonds to the skin to allow for collection and storage of sweat in an interconnected set of microreservoirs. Pressure induced by the sweat glands drives flow through a network of microchannels that incorporates capillary bursting valves designed to open at different pressures, for the purpose of passively guiding sweat through the system in sequential fashion. A representative device recovers 1.8 µL volumes of sweat each from 0.8 min of sweating into a set of separate microreservoirs, collected from 0.03 cm 2 area of skin with approximately five glands, corresponding to a sweat rate of 0.60 µL min −1 per gland. Human studies demonstrate applications in the accurate chemical analysis of lactate, sodium, and potassium concentrations and their temporal variations.