The multiplexing capabilities of instruments such as KMOS have facilitated a huge leap forward in investigating galaxy scaling relations at high redshift. This enabled for instance the KMOS-3D survey that targeted the ionized gas emission of more than 700 galaxies at z=0.6-2.6 with typical integration times of 6-11 hr. Based on this high-quality data set ensuring consistent observation and analysis techniques, we present the evolution of the stellar and baryonic mass Tully-Fisher relations of 135 massive, star-forming galaxies over 3.5 billion years from z~2.3 to z~0.9. With gas-to-stellar mass ratios decreasing towards lower redshift, we find that the contribution of dark matter to the dynamical mass on galactic scales increases. Our result provides one of the corner stones of the recently emerging evidence for strongly baryon-dominated main-sequence galaxies at z≥2.