The origin of rapid rotation in massive stars remains debated, although binary interactions are now often advocated as a cause. However, the broad and shallow lines in the spectra of fast rotators make direct detection of binarity difficult. In this paper, we report on the discovery and analysis of multiplicity for three fast-rotating massive stars: HD 25631 (B3V), HD 191495 (B0V), and HD 46485 (O7V). They display strikingly similar TESS light curves, with two narrow eclipses superimposed on a sinusoidal variation due to reflection effects. We complement these photometric data by spectroscopy from various instruments (X-Shooter, Espadons, FUSE...), to further constrain the nature of these systems. The detailed analyses of these data demonstrates that the companions of the massive OB stars have low masses (~1 M⊙) with rather large radii (2-4 R⊙) and low temperatures (<15 kK). These companions display no UV signature, which would exclude a hot subdwarf nature, but disentangling of the large set of X-Shooter spectra of HD 25631 revealed the typical signature of chromospheric activity in the companion's spectrum. In addition, despite the short orbital periods (P = 3-7 d), the fast-rotating OB-stars still display non-synchronized rotation and all systems appear young (<20 Myr). This suggests that, as in a few other cases, these massive stars are paired in those systems with non-degenerate, low-mass PMS companions, implying that fast rotation would not be a consequence of a past binary interactions in their case.