Incorporating water-based polymer breakers, such as oxidizers, enzymes and/or acids, into a mixture of an oil and oil-soluble surfactants creates an emulsion that can then perform as a dual-functional breaker for reducing the viscosity of hybrid fluids gelled with both a viscoelastic surfactant (VES) and a polymer. The outer phase of the dual-functional breaker emulsion is oil, e.g. a mineral oil, containing an oil-soluble surfactant that will, over time and with heat, break the VES portion of the gel. As it does so, the polymer breaker in the internal aqueous phase will be released to then break the polymer portion of the gel. The polymer breaker will not start to break the polymer gel before the oil-soluble surfactant starts to break the VES gel. The overall breaking using the emulsion is slower as compared to introducing the polymer breaker and the oil-soluble surfactant in a non-emulsified form.