We characterize ionized gas outflows using a large sample of ≃330 high-luminosity [45.5 < log(Lbol/erg s-1) < 49.0], high-redshift (1.5 ≲ z ≲ 4.0) quasars via their [O III]λλ4960,5008 emission. The median velocity width of the [O III] emission line is 1540 kms-1, increasing with increasing quasar luminosity. Broad, blue-shifted wings are seen in the [O III] profiles of ≃42 per cent of the sample. Rest-frame ultraviolet spectra with well-characterized C IVλ1550 emission-line properties are available for more than 210 quasars, allowing an investigation of the relationship between the broad-line region (BLR) and narrow-line region (NLR) emission properties. The [O III] blueshift is correlated with C IV blueshift, even when the dependence of both quantities on quasar luminosity has been taken into account. A strong anticorrelation between the [O III] equivalent width (EW) and C IV blueshift also exists. Furthermore, [O III] is very weak, with EW < 1 Å in ≃10 per cent of the sample, a factor of 10 higher compared to quasars at lower luminosities and redshifts. If the [O III] emission originates in an extended NLR, the observations suggest that quasar-driven winds are capable of influencing the host-galaxy environment out to kilo-parsec scales. The mean kinetic power of the ionized gas outflows is then 1044.7 erg s-1, which is ≃0.15 per cent of the bolometric luminosity of the quasar. These outflow efficiencies are broadly consistent with those invoked in current active galactic nuclei feedback models.