Fresh-cut fruits and vegetables, as near-fresh foods, are a quick and easy solution to a healthy and balanced diet. The rapid degradation of nutritional and sensory quality during the processing and storage of a product is critical and plant-type-dependent. The introduction of disruptive technological solutions in fresh-cut processing, which could maintain fresh-like quality with less environmental impact, is an emerging research concept. The application of abiotic stress treatments (heat shock and UV-C) induces metabolic responses and microbial effects in plant tissues, potentially slowing down several quality senescence pathways. The previously selected combined and single effects of heat shock (100 °C/45 s; in the whole root) and UV-C (2.5 kJ/m2) treatments and two packaging conditions (oriented polypropylene (OPP) vs. micro-perforated OPP films) on controlling critical degradation pathways of fresh-cut carrots and on promoting bioactive and sensory quality during storage (5 °C, 14 days) were studied. Among the tested combinations, synergistic effects on the quality retention of fresh-cut carrots were only attained for applying heat shock associated with micro-perforated OPP film packaging. Its effects on reducing (3.3 Log10 CFU/g) the initial contamination and controlling microbiological spoilage (counts below the threshold limit of 7.5 Log10 CFU/g), increasing the bioactive content (38% and 72% in total phenolic content and chlorogenic acid, respectively), and preserving fresh quality attributes prove to be a viable alternative technology for shredded carrot processing.