We investigate Extremely Red Quasars ( ERQs ) , a remarkable population of heavily-reddened quasars at redshift z \sim 2 - 3 that might be caught during a short-lived ‘ ‘ blow-out ’ ’ phase of quasar/galaxy evolution . We perform a near-IR observational campaign using Keck/NIRSPEC , VLT/X-shooter and Gemini/GNIRS to measure rest-frame optical spectra of 28 ERQs with median infrared luminosity \langle log L ( erg/s ) \rangle \sim 46.2 . They exhibit the broadest and most blue-shifted [ O \sevensize III ] \lambda 4959,5007 emission lines ever reported , with widths ( w _ { 90 } ) ranging between 2053 and 7227 km s ^ { -1 } , and maximum outflow speeds ( v _ { 98 } ) up to 6702 km s ^ { -1 } . ERQs on average have [ O \sevensize III ] outflows velocities about 3 times larger than those of luminosity-matched blue quasar samples . We show that the faster [ O \sevensize III ] outflows in ERQs are strongly correlated with their extreme red colors and not with radio-loudness , larger quasar luminosities , nor higher Eddington ratios . We estimate for these objects that at least 3 - 5 per cent of their bolometric luminosity is being converted into the kinetic power of the observed wind . Our results reveal that ERQs have the potential to strongly affect the evolution of host galaxies .