We report a Karl G. Jansky Very Large Array search for redshifted CO(1–0) emission from three H i-absorption-selected galaxies at z ≈ 2, identified earlier in their CO(3–2) or CO(4–3) emission. We detect CO(1–0) emission from DLA B1228-113 at z ≈ 2.1933 and DLA J0918+1636 at z ≈ 2.5848; these are the first detections of CO(1–0) emission in high-z H i-selected galaxies. We obtain high molecular gas masses, M mol ≈ 1011 × (α CO/4.36) M ⊙, for the two objects with CO(1–0) detections, which are a factor of ≈1.5–2 lower than earlier estimates. We determine the excitation of the mid-J CO rotational levels relative to the J = 1 level, r J1, in H i-selected galaxies for the first time, obtaining r 31 = 1.00 ± 0.20 and r 41 = 1.03 ± 0.23 for DLA J0918+1636, and r 31 = 0.86 ± 0.21 for DLA B1228-113. These values are consistent with thermal excitation of the J = 3 and J = 4 levels. The excitation of the J = 3 level in the H i-selected galaxies is similar to that seen in massive main-sequence and submillimeter galaxies at z≳2, but higher than that in main-sequence galaxies at z ≈ 1.5; the higher excitation of the galaxies at z ≳ 2 is likely to be due to their higher star formation rate (SFR) surface density. We use Hubble Space Telescope Wide Field Camera 3 imaging to detect the rest-frame near-ultraviolet (NUV) emission of DLA B1228-113, obtaining an NUV SFR of 4.44 ± 0.47 M ⊙ yr−1, significantly lower than that obtained from the total infrared luminosity, indicating significant dust extinction in the z ≈ 2.1933 galaxy.