The production of graphene through anodic exfoliation of graphite in water is regarded as a competitive approach in the efforts to scale-up the manufacturing of this two-dimensional material for different practical uses. However, issues related to oxidative attack of the nanosheets inherent to this delamination process have traditionally precluded the attainment of high quality materials, with the use of proper electrolyte additives as oxidation-preventing agents being proposed as a possible way out. Here we demonstrate that sodium chloride (table salt) can be used as a highly efficient additive (co-electrolyte) of common sulfate-based electrolytes, yielding anodically exfoliated graphene with minimal oxidation (O/C ratio ∼0.02–0.03) and thus a high structural quality. As an oxidation-preventing co-electrolyte, sodium chloride clearly outperformed other tested additives, including sodium borohydride, sulfite, citrate, bromide and iodide, ascorbic acid or ethanol, as well as other recently reported chemical species of a more complex nature and/or less readily available. The apparently contradicting ability of the chloride anion to avert oxidation of anodic graphene without negatively interfering with the exfoliation process itself was also discussed and ultimately ascribed to the different chemical reactivity of graphite edges and basal planes. The as-prepared, low-oxidized graphene exhibited a notable adsorption capacity toward organic dyes in aqueous solution (e.g., ∼450mgg−1 for methyl orange), a substantial ability to absorb oils and non-polar organic solvents (15–30gg−1), and displayed a good capacitive energy storage behavior (e.g., ∼120Fg−1 at 0.1Ag−1), all without the need of any post-processing steps that are so common for graphene-based materials. Overall, the demonstration that low-oxidized anodic graphene can be obtained by resorting only to inexpensive and widely available reagents should facilitate the implementation of this methodology in the industrial manufacturing of high quality graphene for several applications.