This paper investigates the intersection of income and race in structuring access to higher education among students that participate in a national high-stakes exam in Brazil. Our objectives are (i) to estimate the probability of students coming from different income strata, racial groups, and performance levels to access higher education and (ii) to decompose income and racial effects into direct (net of educational performance) and indirect effects (through educational performance). Our data comes from a panel of high school graduates tracked between 2012 and 2017 and allow us to describe the following findings. Firstly, the probability of entering higher education is always higher among candidates from higher income strata. Second, there is a convergence in admission probabilities across the performance scale. Third, the admission curve across a performance scale is much steeper among applicants from low-income strata compared to richer students. In all of these results, students self-identified as black, brown, or indigenous (BBI) are less likely to transition to higher education than whites, even though they are in the same income and performance strata. We suggest that students from privileged socioeconomic backgrounds benefit from alternative entry strategies, such as paying tuition at less competitive private colleges. For students from low-income strata, the main alternative for entering higher education is through high academic performance. By decomposing racial effects, we show the cumulative effect of racial stratification; the gap between white and BBI students is both related to higher propensity of transitioning to higher education and higher educational performance.