Wounds, disruptions in normal anatomy, are classified as acute or chronic. The choice of wound treatment relies significantly on dressing materials. Electrospun nanofibrous materials offer promising applications in wound healing, featuring a substantial surface area, close mimicry of the natural extracellular matrix, and adjustable water resistance, air permeability, and drug release. This research endeavors to formulate an innovative three-layered nanofibrous wound dressing using the electrospinning technique with the primary objectives of enhancing patient well-being, exhibiting antimicrobial characteristics, and expediting wound healing. The designed dressing comprises nanofibers of polyurethane (PU), quercetin (Q)-loaded polyethylene glycol (PEG), polyvinyl alcohol (PVA), and gelatin. Characterization of individual layers and the integrated wound dressing was conducted through SEM and FT-IR analyses. The efficacy of the nanofibrous wound dressing was assessed through in vitro human cell culture and in vivo rat wound models. The anti-toxic effects of nanofiber wound dressing on human epithelial and keratin cells have been proven. In vitro wound models in 24-well plates were utilized to assess the impact on wound healing rates. Photographic documentation of wound closure was performed at the different treatment hours, revealing complete closure of the wounds by the end of the 48th hour. Rats with 2 × 1 cm wounds were treated with the nanofibrous dressings, and wound healing progress was observed over a 14-day period. qRT-PCR was employed to analyze MMP-9, TIMP1, COL1A1, PDGFA, and VEGFC mRNA expressions. With its contemporary design surpassing existing treatments, the nanofiber wound dressing stands out for its wound-healing acceleration and antibacterial properties.