Quinnipiac University, a small school best known for political polls, is beating the biggest names in higher education at investing with the help of an unlikely force: the stock picker.

The private university tucked away in the Connecticut hills delivered annualized gains of 6.1% for the decade ended June 30, 2017. The returns are in the top 10% of U.S. schools ranked by the National Association of College and University Business Officers and Commonfund.

John...