Individuals of lower socioeconomic position (SEP) experience a greater rate of alcohol-related harms, yet they consume equal or lower amounts of alcohol than higher-SEP individuals. This phenomenon, called the “alcohol harm paradox” (AHP), gained attention recently, and different mechanisms have been proposed to explain it. Since both SEP and alcohol have been suggested to be associated with periodontitis risk, we conducted a secondary analysis using data from the National Health and Nutrition Examination Survey 2011 to 2012 and 2013 to 2014 cycles, aiming to examine 1) whether the association between alcohol consumption and periodontitis is modified by SEP and 2) the extent to which the effect of SEP inequalities on periodontitis is mediated by and/or interacts with alcohol consumption. We set educational attainment as the main SEP proxy and tested the poverty income ratio in subsequent sensitivity analyses. Effect measure modification analysis was employed, considering heavy drinking as exposure, and causal mediation analysis based on the potential outcome’s framework decomposed the effect of SEP on periodontitis in proportions attributable to mediation and interaction. Models were fitted using binary logistic regression and adjusted for sex, ethnicity, age, body mass index, smoking status, diabetes, binge drinking, and regular preventive dental visits. The analytical sample comprised 4,057 participants. After adjusting for covariates, less educated heavy drinkers presented 175% (odds ratio, 2.75; 95% confidence interval [CI], 2.04–3.72) higher odds of periodontitis than their counterparts, and super-additive associations were found (relative excess risk due to interaction: 1.35; 95% CI, 0.49–2.20). Additionally, −69.5% (95% CI, −122.1% to −16.8%) of the effects of education on periodontitis were attributable to interaction with heavy drinking, consistent with the AHP. No contribution was found for the mechanism of mediation. Heavy drinking disproportionately impacts the occurrence of periodontitis in lower-SEP individuals. Lower-SEP individuals seem to experience differential effects of heavy drinking on periodontitis.