We present Period-Luminosity and Period-Luminosity-Color relations at maximum light for Mira variables in the Magellanic Clouds using time-series data from the Optical Gravitational Lensing Experiment (OGLE-III) and Gaia data release 2. The maximum-light relations exhibit a scatter typically up to ∼30% smaller than their mean-light counterparts. The apparent magnitudes of oxygen-rich Miras at maximum light display significantly smaller cycle-to-cycle variations than at minimum light. High-precision photometric data for Kepler Mira candidates also exhibit stable magnitude variations at the brightest epochs, while their multi-epoch spectra display strong Balmer emission lines and weak molecular absorption at maximum light. The stability of maximum-light magnitudes for Miras possibly occurs due to the decrease in the sensitivity to molecular bands at their warmest phase. At near-infrared wavelengths, the period-luminosity relations (PLRs) of Miras display similar dispersion at mean and maximum light with limited time-series data in the Magellanic Clouds. A kink in the oxygen-rich Mira PLRs is found at 300 days in the VI-bands, which shifts to longer periods (∼350 days) at near-infrared wavelengths. Oxygen-rich Mira PLRs at maximum light provide a relative distance modulus, Δμ = 0.48 ± 0.08 mag, between the Magellanic Clouds with a smaller statistical uncertainty than the mean-light relations. The maximum-light properties of Miras can be very useful for stellar atmosphere modeling and distance scale studies provided their stability and the universality can be established in other stellar environments in the era of extremely large telescopes.