Economical and nanomolar-level determination of the analgesic drug, acetaminophen (APAP), is reported in this work. A novel ternary nanocomposite based on silver-doped sugar apple-like cupric oxide (CuO)-decorated amine-functionalized multi-walled carbon nanotubes (fCNTs) was sonochemically prepared. CuO nanoparticles were synthesized based on the ascorbic acid-mediated low-temperature method, and sidewall functionalization of CNTs was carried out. Important characterizations of the synthesized materials were analyzed using SEM, TEM, HAADF-STEM, elemental mapping, EDX, lattice fringes, SAED pattern, XRD, EIS, UV-Vis, micro-Raman spectroscopy, and FTIR. It was noted the sonochemically prepared nanocomposite diligently fabricated on screen-printed carbon electrode showcased outstanding electrocatalytic performance towards APAP determination. The APAP sensor exhibited ultra-low limit of detection of 4 nM, wide linear concentration ranges of 0.02–3.77 and 3.77–90.02 μM, and high sensitivity of 30.45 μA μM−1 cm−2. Moreover, further evaluation of the sensor’s performance based on electrochemical experiments showcased outstanding selectivity, stability, reproducibility, and repeatability. Further, excellent practical feasibility of the proposed APAP sensor was affirmed with excellent recovery larger than 96.86% and a maximum RSD of 3.67%.