The Minimal Supersymmetric Standard Model (MSSM) is under intense scrutiny at the LHC and in dark matter searches. Interestingly, scenarios with light squarks of the third generation remain not only viable, but also well motivated by the observed Standard-Model-like Higgs boson mass and dark matter relic density. The latter often requires important contributions from squark pair annihilation. Following up on previous work, we present in this paper a precision analysis of squark pair annihilation into quarks at next-to-leading order of QCD including Sommerfeld enhancement effects. We discuss all technical details of our one-loop, real emission and resummation calculations, their implementation in the precision tool DM@NLO, as well as the numerical impact on the annihilation cross section and cosmological relic density in phenomenological MSSM scenarios respecting in particular current LHC constraints. We demonstrate that including these radiative corrections leads to substantial shifts in the preferred parameter regions by up to 20 GeV.