The objective of this study was to introduce a combined sparse sampling and stochastic expansion approach for efficient and accurate uncertainty quantification. The new techniques are applied to high-fidelity, hypersonic reentry flow simulations, which may contain large numbers of aleatory and epistemic uncertainties. Stochastic expansion coefficients were obtained using the point-collocation nonintrusive polynomial chaos technique with a number of samples less than the minimum number required for a total-order expansion. This study introduced two methods of measuring the accuracy of the expansion coefficients, as well as their convergence with iteratively increasing sample size. The newly developed approaches were demonstrated on two model problems. The first was a model for stagnation point, convective heat transfer in hypersonic flow. Mixed uncertainty quantification analysis results showed that accurate expansion coefficients could be obtained with half of the minimum number of samples required for a total-order expansion. The second problem was a high-fidelity, computational fluid dynamics model for radiative heat flux prediction on a hypersonic inflatable aerodynamic decelerator during Mars entry. The model consisted of 93 uncertain parameters, coming from both flowfield and radiation modeling. Results indicated that an accurate surrogate model could be obtained with only about 15% of the number of samples required for a total-order expansion when compared with previous work.