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Parametric amplifiers have allowed breakthroughs in ultrafast, strong-field, and high-energy density laser science and are an essential tool for extending the frequency range of powerful emerging diode-pumped solid-state laser technology. However, their impact is limited by inherently low quantum efficiency due to nonuniform light extraction. Here we demonstrate a new type of parametric amplifier based on hybridized nonlinear optics. Hybridization of parametric amplification with idler second harmonic generation induces unusual evolution dynamics for a fully parametric amplifier - with saturating rather than cyclic gain - observed here for the first time. This allows highly uniform light extraction enabling unprecedented efficiency for a lossless amplifier with Gaussian-like intensity profiles - a 48-dB single-stage gain with 68% quantum efficiency and 44% pump-to-signal energy conversion - a several-fold improvement over the standard. Possessing both laser-like high quantum efficiency and the advantages of thermal-loading free parametric systems, this simple approach can be implemented widely and have significant impact by increasing several-fold the power available for science and industry.