Drug assays with patient-derived cells such as circulating tumor cells requires manipulating small sample volumes without loss of rare disease-causing cells. Here, we report an effective technology for isolating and analyzing individual tumor cells and their clusters from minute sample volumes using an optimized microfluidic device integrated with pipettes. The method involves using hand pipetting to create an array of cell-laden nanoliter-sized droplets immobilized in a microfluidic device without loss of tumor cells during the pipetting process. Using this technology, we demonstrate single-cell analysis of tumor cell response to the chemotherapy drug doxorubicin. We find that even though individual tumor cells display diverse uptake profiles of the drug, the onset of apoptosis is determined by accumulation of a critical intracellular concentration of doxorubicin. Experiments with clusters of tumor cells compartmentalized in microfluidic drops reveal that cells within a cluster have higher viability than their single-cell counterparts when exposed to doxorubicin. This result suggests that circulating tumor cell clusters might be able to better survive chemotherapy drug treatment. Our technology is a promising tool for understanding tumor cell-drug interactions in patient-derived samples including rare cells.