ABSTRACT Understanding the links between different phases of outflows from active galactic nuclei is a key goal in extragalactic astrophysics. Here, we compare [O iii] $\lambda \lambda$4960, 5008 outflow signatures in quasars with and without broad absorption lines (BALs), aiming to test how the broad absorption troughs seen in the rest-frame ultraviolet are linked to the narrow line region outflows seen in the rest-frame optical. We present new near-infrared spectra from Magellan/FIRE that cover [O iii] in 12 quasars with $2.1\lt z\lt 2.3$, selected to have strong outflow signatures in C iv$\lambda$1550. Combining with data from the literature, we build a sample of 73 BAL, 115 miniBAL, and 125 non-BAL quasars with $1.5\lt z\lt 2.6$. The strength and velocity width of [O iii] correlate strongly with the C iv emission properties, but no significant difference is seen in the [O iii] emission-line properties between the BALs, non-BALs, and miniBALs once the dependence on C iv emission is taken into account. A weak correlation is observed between the velocities of C iv BALs and [O iii] emission, which is accounted for by the fact that both outflow signatures correlate with the underlying C iv emission properties. Our results add to the growing evidence that BALs and non-BALs are drawn from the same parent population and are consistent with a scenario wherein BAL troughs are intermittent tracers of persistent quasar outflows, with a part of such outflow becoming optically thick along our line of sight for sporadic periods of time within which BALs are observed.