The spectral and transport properties of strongly correlated metals, such as SrVO (SVO), are widely attributed to electron-electron (-) interactions, with lattice vibrations (phonons) playing a secondary role. Here, using first-principles electron-phonon (-ph) and dynamical mean field theory calculations, we show that -ph interactions play an essential role in SVO: they govern the electron scattering and resistivity in a wide temperature range down to 30 K, and induce an experimentally observed kink in the spectral function. In contrast, the - interactions control quasiparticle renormalizations and low temperature transport, and enhance the -ph coupling. We clarify the origin of the near temperature dependence of the resistivity by analyzing the - and -ph limited transport regimes. Our work disentangles the electronic and lattice degrees of freedom in a prototypical correlated metal, revealing the dominant role of -ph interactions in SVO.