One of the great challenges in cellular studies is to develop a rapid and biocompatible analytical tool for single-cell analysis. We report a rapid, DNA nanostructure-supported aptamer pull-down (DNaPull) assay under convective flux in a glass capillary for analyzing the contents of droplets with nano- or picoliter volumes. We have demonstrated that the scaffolded aptamer can greatly improve the efficiency of target molecules' pull down. The convective flux allows complete reaction in <5 min, which is an 18-fold improvement compared to purely diffusive flux (traditional model of the stationary case). This established DNaPull assay can serve as a rapid and sensitive analytical platform for analyzing a variety of bioactive molecules, including small molecules [ATP, limit of detecton (LOD) of 1 μM], a drug (cocaine, LOD of 1 μM), and a biomarker (thrombin, LOD of 0.1 nM). Significantly, the designed microfluidic device compartmentalizes live cells into nanoliter-sized droplets to present single-cell samples. As a proof of concept, we demonstrated that cellular molecules (ATP) from a discrete number of HNE1 cells (zero to five cells) lysed inside nanoliter-sized droplets can be analyzed using our DNaPull assay, in which the intracellular ATP level was estimated to be ∼3.4 mM. Given the rapid assay feature and single-cell sample analysis ability, we believe that our analytical platform of convection-driven DNaPull in a glass capillary can provide a new paradigm in biosensor design and will be valuable for single-cell analysis.