It is well-established that the combined use of nanostructured substrates and immunoaffinity agents can enhance the cell-capture performance of the substrates, thus offering a practical solution to effectively capture circulating tumor cells (CTCs) in peripheral blood. Developing along this strategy, this study first demonstrated a top-down approach for the fabrication of tetrahedral DNA nanostructure (TDN)-NanoGold substrates through the hierarchical integration of three functional constituents at various length-scales: a macroscale glass slide, sub-microscale self-organized NanoGold, and nanoscale self-assembled TDN. The TDN-NanoGold substrates were then assembled with microfluidic chaotic mixers to give TDN-NanoGold Click Chips. In conjunction with the use of copper (Cu)-catalyzed azide-alkyne cycloaddition (CuAAC)-mediated CTC capture and restriction enzyme-triggered CTC release, TDN-NanoGold Click Chips allow for effective enumeration and purification of CTCs with intact cell morphologies and preserved molecular integrity. To evaluate the clinical utility of TDN-NanoGold Click Chips, we used these devices to isolate and purify CTCs from patients with human papillomavirus (HPV)-positive (+) head and neck squamous cell carcinoma (HNSCC). The purified HPV(+) HNSCC CTCs were then subjected to RT-ddPCR testing, allowing for detection of E6/E7 oncogenes, the characteristic molecular signatures of HPV(+) HNSCC. We found that the resulting HPV(+) HNSCC CTC counts and E6/E7 transcript copy numbers are correlated with the treatment responses in the patients, suggesting the potential clinical utility of TDN-NanoGold Click Chips for non-invasive diagnostic applications of HPV(+) HNSCC.