© 2016. The American Astronomical Society. All rights reserved.. Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three core programs in the Sloan Digital Sky Survey-IV, is an integral-field spectroscopic survey of roughly 10,000 nearby galaxies. It employs dithered observations using 17 hexagonal bundles of 2″ fibers to obtain resolved spectroscopy over a wide wavelength range of 3600-10300 . To map the internal variations within each galaxy, we need to perform accurate spectral surface photometry, which is to calibrate the specific intensity at every spatial location sampled by each individual aperture element of the integral field unit. The calibration must correct only for the flux loss due to atmospheric throughput and the instrument response, but not for losses due to the finite geometry of the fiber aperture. This requires the use of standard star measurements to strictly separate these two flux loss factors (throughput versus geometry), a difficult challenge with standard single-fiber spectroscopy techniques due to various practical limitations. Therefore, we developed a technique for spectral surface photometry using multiple small fiber-bundles targeting standard stars simultaneously with galaxy observations. We discuss the principles of our approach and how they compare to previous efforts, and we demonstrate the precision and accuracy achieved. MaNGA's relative calibration between the wavelengths of Hα and Hβ has an rms of 1.7%, while that between [N ii] λ6583 and [O ii] λ3727 has an rms of 4.7%. Using extinction-corrected star formation rates and gas-phase metallicities as an illustration, this level of precision guarantees that flux calibration errors will be sub-dominant when estimating these quantities. The absolute calibration is better than 5% for more than 89% of MaNGA's wavelength range.