The integration of fluidics and optics, as in flow-through nanohole arrays, has enabled increased transport of analytes to sensing surfaces. Limits of detection, however, are fundamentally limited by local analyte concentration. We employ the nanohole array geometry and the conducting nature of the film to actively concentrate analyte within the sensor. We achieve 180-fold enrichment of a dye, and 100-fold enrichment and simultaneous sensing of a protein in less than 1 min. The method presents opportunities for an order of magnitude increase in sensing speed and 2 orders of magnitude improvement in limit of detection.