Polychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs) remain of particular concern owing to their extensive toxicity towards health and accumulation in the environment. Atmospheric oxidation (by ambient oxygen molecules) of this class of persistent environmental pollutants has little to no kinetic feasibility due to very sizable activation energies in the entrance channel. The current control measures involve energy-intensive source incineration of contaminated materials at high temperatures as high as 850 °C. This study finds an alternative low-energy approach of destroying dioxin-like compounds, proposing that advanced oxidation by highly reactive singlet oxygen (O2 1Δg, originated from chemical, surface-mediated and photochemical processes) can initiate low-temperature remediation of these pollutants. This contribution completes the first milestone in mapping out the mechanisms of the electrophilic addition of singlet oxygen to unsubstituted and chlorinated dibenzo-p-dioxin (DBD) and dibenzofuran (DBF) structures, according to density functional theory DFT-B3LYP method in conjunction with the 6–311+g(d,p) basis set, as well as energy refinements based on the approximate spin-projection scheme. The [2+2]-cycloaddition mechanism appears dominant for singlet oxidation of dibenzo-p-dioxin with a fitted rate constant of k(T) = 5.01 × 10−14 exp(-98000/RT). On the other hand, the addition of singlet oxygen to the aromatic ring of dibenzofuran primarily transpires via [4+2]-cycloaddition channel with a fitted rate constant of k(T) = 2.16 × 10−13 exp(-119000/RT). The results suggest that application of singlet oxygen can reduce the energy cost of recycling halogenated and flame retarded materials.