We present the discovery and characterization of four low-mass (M < 0.6 M⊙ eclipsing binary (EB) systems in the sub-Gyr old Praesepe open cluster using Kepler/K2 time series photometry and Keck/HIRES spectroscopy. We present a new Gaussian process EB model, GP–EBOP, as well as a method of simultaneously determining effective temperatures and distances for EBs. Three of the reported systems (AD 3814, AD 2615 and AD 1508) are detached and double-lined, and precise solutions are presented for the first two. We determine masses and radii to 1%–3% precision for AD 3814 and to 5%–6% for AD 2615. Together with effective temperatures determined to ~50 K precision, we test the PARSEC v1.2 and BHAC15 stellar evolution models. Our EB parameters are more consistent with the PARSEC models, primarily because the BHAC15 temperature scale is hotter than our data over the mid-M-dwarf mass range probed. Both ADs 3814 and 2615, which have orbital periods of 6.0 and 11.6 days, are circularized but not synchronized. This suggests that either synchronization proceeds more slowly in fully convective stars than the theory of equilibrium tides predicts, or magnetic braking is currently playing a more important role than tidal forces in the spin evolution of these binaries. The fourth system (AD 3116) comprises a brown dwarf transiting a mid-M-dwarf, which is the first such system discovered in a sub-Gyr open cluster. Finally, these new discoveries increase the number of characterized EBs in sub-Gyr open clusters by 20% (40%) below M < 1.5 M⊙ (M < 0.6 M⊙).