Some of the most important processes in nature involve interfacial water. It has long been conjectured that specific ion effects therein are associated with the unique properties of interfacial water. Here we reveal the mechanism of such association by showing that the strength of ion-specific long-range correlations tracks the amplification of fluctuations on the surface of water-alcohol mixtures at the percolation thresholds of their hydrogen-bonded water networks. We used in situ online electrospray mass spectrometry to determine chi = [I-]/[Br-] ratios in microfilms of (NaI + NaBr) solutions in water-methanol (ME) and water-isopropanol (IP) mixtures as functions of x(ME) and x(IP) molar fractions, and the addition of NaClO4. We found that, beginning at 0.1 mu M, ClO4- has detectable effects on chi that peak at x(ME) similar to 0.40, x(IP) similar to 0.15, i.e., at water percolation thresholds where fluctuations maximize mean water cluster sizes and, hence, interionic connections. The stronger correlations between ions of similar surface propensities suggest that correlations propagate preferentially along 2-D interfacial layers.