Overeducation is indicative of a suboptimal education–job match and is related to several negative consequences for workers. Despite extensive research explaining the overeducation phenomenon, previous studies have not simultaneously analyzed educational background (i.e., educational degrees) and social background effects, or have failed to consider both the vertical and horizontal dimension that educational degrees entail (i.e., level and field). This article seeks to overcome these limitations by examining whether overeducation varies (1) across educational background (considering both level and field of educational degrees), (2) across social background, and (3) by social background among workers with the same degree. Based on the German BIBB/BAuA Employment Survey 2018, results suggest that highly educated workers are more likely to be overeducated for the jobs they hold, implying the supply of this workforce exceeds the available adequate jobs on the German labor market. The field of education determines the risk of overeducation as well, with some occupationally specific fields of education (IT, natural sciences, and health) making for lower overeducation risk for both vocational and academic education. The results also indicate social background directly influences education–job matches (controlling for level and field of education), i.e., a social gap in overeducation. This evidence suggests an effect of social background on job allocation processes, beyond the effect of education, so that the offspring of privileged classes (i.e., high salariat) use the same degrees on the labor market more profitably than the offspring of less privileged classes. Given the low attention paid to education–job matches in social stratification analyses, the present article makes a noteworthy contribution to the literature on social stratification and inequality. In addition, the present research will serve as a base for future studies on overeducation including both the vertical and horizontal dimension of educational degrees.