We present analytical results for the leading top-Yukawa and QCD contribution to the β-function for the Higgs self-coupling λ of the Standard Model at four-loop level, namely the part ∝ yt4gs6 independently confirming a result given in . We also give the contribution ∝ yt2gs6 of the anomalous dimension of the Higgs field as well as the terms ∝ ytgs8 to the top-Yukawa β-function which can also be derived from the anomalous dimension of the top quark mass. We compare the results with the RG functions of the correlators of two and four scalar currents in pure QCD and find a new relation between the anomalous dimension γ0 of the QCD vacuum energy and the anomalous dimension γSS appearing in the RG equation of the correlator of two scalar currents. Together with m the recently computed top-Yukawa and QCD contributions to βgs [2, 3] the β-functions presented here constitute the leading four-loop contributions to the evolution of the Higgs self-coupling. A numerical estimate of these terms at the scale of the top-quark mass is presented as well as an analysis of the impact on the evolution of λ up to the Planck scale and the vacuum stability problem.