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We present rest-frame near-ultraviolet (NUV) spectroscopy of star-forming galaxies (SFGs) at 0.6 < z < 1.2 from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) in SDSS-IV. One of the eBOSS programs is to obtain 2" (about 15 kpc) fiber spectra of about 200,000 emission-line galaxies (ELGs) at redshift z ≳ 0.6. We use the data from the pilot observations of this program, including 8620 spectra of SFGs at 0.6 < z < 1.2. The median composite spectra of these SFGs at 2200 Å < λ < 4000 Å feature asymmetric, preferentially blueshifted non-resonant emission, Fe ii*, and blueshifted resonant absorption, e.g., Fe ii and Mg ii, indicating ubiquitous outflows driven by star formation at these redshifts. For the absorption lines, we find a variety of velocity profiles with different degrees of blueshift. Comparing our new observations with the literature, we do not observe the non-resonant emission in the small-aperture (<40 pc) spectra of local star-forming regions with the Hubble Space Telescope, and find the observed line ratios in the SFG spectra to be different from those in the spectra of local star-forming regions, as well as those of quasar absorption-line systems in the same redshift range. We introduce an outflow model that can simultaneously explain the multiple observed properties and suggest that the variety of absorption velocity profiles and the line ratio differences are caused by scattered fluorescent emission filling in on top of the absorption in the large-aperture eBOSS spectra. We develop an observation-driven, model-independent method to correct the emission infill to reveal the true absorption profiles. Finally, we show that the strengths of both the non-resonant emission and the emission-corrected resonant absorption increase with [O ii] λλ3727, 3730 rest equivalent width and luminosity, with a slightly larger dependence on the former. Our results show that the eBOSS and future dark-energy surveys (e.g., Dark Energy Spectroscopic Instrument survey and Prime Focus Spectrograph survey) will provide rich data sets of rest-frame NUV spectroscopy for astrophysical applications.