In 1947, he played in Kentucky's first bowl game, a 24-14 win against Villanova University in the 1947 Great Lakes Bowl. He got married after his junior year and Bryant revoked his football scholarship. Ulinski considered transferring to Eastern Kentucky University to play basketball, but changed his mind after the marriage rule was rescinded.
In 1947, he took part in Kentucky's first postseason game, a 24-14 win over Villanova University in the Great Lakes Bowl. He married after his junior year and Bryant canceled his football scholarship. Ulinski thought about transferring to Eastern Kentucky University for basketball but decided against it when the marriage rule was lifted.