We investigate the implications of the Higgs rate measurements from Run 1 of the LHC for the mass of the light scalar top partner (stop) in the Minimal Supersymmetric Standard Model (MSSM). We focus on light stop masses, and we decouple the second, heavy stop and the gluino to the multi-TeV range in order to obtain a Higgs mass of around 125 GeV. We derive lower mass limits for the light stop within various scenarios, taking into account the effects of a possibly light scalar tau partner (stau) or chargino on the Higgs rates, of additional Higgs decays to undetectable new physics, as well as of non-decoupling of the heavy Higgs sector. Under conservative assumptions, the stop can be as light as 123 GeV. Relaxing certain theoretical and experimental constraints, such as vacuum stability and model-dependent bounds on sparticle masses from LEP, we find that the light stop mass can be as light as 116 GeV. Our indirect limits are complementary to direct limits on the light stop mass from collider searches and have important implications for electroweak baryogenesis in the MSSM as a possible explanation for the observed matter-antimatter asymmetry of the Universe.