Using integral field spectroscopy, we demonstrate that gravity-sensitive absorption features in the zJ-band (0.9--1.35 micron) can constrain the low-mass stellar initial mass function (IMF) in the cores of two elliptical galaxies, M85 and M87. Compared to the visible bands, the near-infrared (NIR) is more sensitive to light from low-mass dwarf stars, whose relative importance is the primary subject of the debate over IMF variations in nearby galaxies. Our analysis compares the observed spectra to the latest stellar population synthesis models by employing two different methods: equivalent widths and spectral fitting. We find that the IMF slopes in M85 are similar to the canonical Milky Way IMF with a median IMF-mismatch parameter $alpha_{K} = 1.26$. In contrast, we find that the IMF in M87 is steeper than a Salpeter IMF with $alpha_{K} = 2.77$. The derived stellar population parameters, including the IMF slopes, are consistent with those from recent results in the visible bands based on spectroscopic and kinematic techniques. Certain elemental abundances, e.g. Na and Fe, have dramatic effects on the IMF-sensitive features and therefore the derived IMF slopes. We show evidence for a high [Na/H] $sim$ 0.65 dex in the core of M85 from two independent ion{Na}{1} absorption features. The high Na abundance may be the result of a recent galactic merger involving M85. This suggests that including [Na/H] in the stellar population model parameters is critical for constraining the IMF slopes in M85. These results confirm the viability of using NIR absorption features to investigate IMF variation in nearby galaxies.