This work describes a new electrochemical biosensor for the simultaneous determination of catechol and hydroquinone. A laccase biorecognition layer was deposited using an innovative soft plasma polymerization technique onto a multiwalled carbon nanotube (MWCNT)-modified glassy carbon electrode (GCE) to sufficiently separate catechol (CT) and hydroquinone (HQ) oxidation peaks. The electrochemical analysis carried out for MWCNTs with various morphologies was supported by density functional theory (DFT) calculations showing differences in the electronic structures of both dihydroxybenzene isomers and the MWCNTs forming the biosensor interlayer. The best biosensor peak separation and biosensor analytical parameters were observed for the device containing 75 μg of MWCNTs with a higher internal diameter. For this laccase-based biosensor, a linearity range from 0.1 to 57 μM for catechol and 0.5 to 57 μM for hydroquinone as well as a sensitivity of 0.56 and 0.54 μA/μM for catechol and hydroquinone was observed, respectively. The limit of detection (LOD) values were 0.028 and 0.15 μM for CT and HQ, respectively. This biosensor was also characterized by good selectivity, stability, and reproducibility. It was successfully applied for the quantification of contaminants in the analysis of natural water samples.