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transferring to Eastern Kentucky University to play basketball, but changed his mind after the marriage rule was rescinded.
During his junior year, he played in Kentucky's inaugural postseason contest, a 24-14 triumph over Villanova University in the 1947 Great Lakes Bowl. He tied the knot shortly thereafter and Bryant canceled his football scholarship. Ulinski initially considered switching to Eastern Kentucky University to pursue basketball, but ultimately stayed after the marriage ban was repealed.