Background/Objectives: Paracetamol is a widely analgesic and antipyretic drug; however, its limited anti-inflammatory efficacy and safety concerns motivate the search for novel non-opioid alternatives. In this study, a series of 4-hydroxyphenylamino-naphthoquinones were designed as paracetamol-inspired analogs and synthesized via a solvent-free, silica-assisted Michael addition, providing a sustainable and efficient synthetic route. Methods: The compounds were evaluated using an integrated strategy combining in silico prediction, density functional theory calculations, molecular docking, ADMET profiling, and in vivo phenotypic pharmacological assays. Results: In vivo evaluation revealed pronounced peripheral antinociceptive activity in the acetic acid-induced writhing model and robust anti-inflammatory effects in carrageenan-induced paw edema, comparable to those of naproxen. These findings suggest a predominantly peripheral mechanism consistent with anti-inflammatory and antinociceptive profiles linked to cyclooxygenase inhibition. A normalization-based multi-criteria analysis integrating peripheral, anti-inflammatory, central, and antipyretic endpoints enabled transparent phenotypic prioritization within the series. Under this framework, compound 7 emerged as the most balanced peripheral–anti-inflammatory candidate, whereas compound 8, evaluated experimentally as a regioisomeric mixture, showed comparatively stronger central antinociceptive activity in the hot plate test. Antipyretic activity in an LPS-induced fever model was limited and not sustained. Conclusions: Overall, these findings indicated that the 4-hydroxyphenylamino-naphthoquinone scaffold emerges as a promising non-opioid platform for peripheral inflammatory pain, supporting further investigation of its pharmacological and mechanistic properties.