We demonstrate second-harmonic generation with ultranarrow resonances in hybrid plasmon-fiber cavities, formed by depositing single-crystalline gold nanorods onto the surface of tapered microfibers with diameters in the range of 1.7-1.8 μm. The localized surface plasmon mode of the single gold nanorod efficiently couples with a whispering gallery mode of the fiber, resulting in a very narrow hybrid plasmon-fiber resonance with a high quality factor Q of up to 250. When illuminated with a tunable 100 fs laser, a sharp SHG peak narrower than half of the spectral width of the impinging laser emerges, superimposed on a broad multiphoton photoluminescence background. The enhancement of the SHG peak of the hybrid system is typically 1000-fold when compared to that of a single gold nanorod alone. Tuning the laser over the hybrid resonance enables second-harmonic spectroscopy and yields an ultranarrow line width as small as 6.4 nm. We determine the second-harmonic signal to rise with the square of the laser power, while the multiphoton photoluminescence background rises with powers between 4 and 6, indicating a very efficient higher-order process. A coupled anharmonic oscillator model is able to describe the linear as well as second-harmonic resonances very well. Our work will open the door to the simultaneous utilization of narrow whispering gallery resonances together with high plasmonic near-field enhancement and should allow for nonlinear sensing and extremely efficient nonlinear light generation from ultrasmall volumes.