Herein, the nanofabrication and characterization of new conductive materials, PANI-CoPc-fur (1) ((PANI = polyaniline and CoPc-fur = tetra-4-(furan-2-methylthiophthalocyaninato)Co(II)) and PANI-CoPc-fur-f-MWCNTs (2) (f-MWCNTs = carboxylic acid-functionalized multiwalled carbon nanotubes), are reported. Subsequently, an electrospun nanofiber (ENF) composite of 2, encapsulated with a poly(vinyl acetate) shell, was fabricated. The resultant core-shell nanoconjugated fibers, ENFs-2, were adsorbed on a glassy carbon electrode (GCE), followed by the immobilization of a permeable adhesion top layer of Nafion (Nf) to render the chemically modified electrode, GCE|ENFs-2-Nf. The electron-mediating properties of the components within the film of GCE|ENFs-2-Nf synergistically aided in promoting its electrocatalytic activities. Consequently, the CME showed greater cyclic voltammetry (CV) peak currents compared to the bare GCE and other modified electrodes, indicating its higher sensitivity toward acetaminophen (APAP), an emerging water pollutant of concern. The detection of APAP at the GCE|ENFs-2-Nf attained by square-wave voltammetry (SWV) was linear from 10 to 200 μM of APAP and was reproducible (%RSD of 3.2%, N = 3). The respective calculated limits of detection and quantification (LOD and LOQ) values of 0.094 and 0.28 μM were lower than those acquired using other electrochemical techniques. Analysis of APAP in the presence of commonly associated interferences metronidazole (MTZ) and dopamine (DA) illustrated a significant separation between the SWV peak potentials of APAP and MTZ, whereas there was some degree of overlap between the SWV current responses of APAP and DA. The analytical performance of the GCE|ENFs-2-Nf rendered a comparable percentage recovery (104%) with that of liquid chromatography-mass spectrometry (LC-MS) (106%).