The Detroit Tigers selected Ujdur in the fourth round of the 1978 MLB Draft. He spent a few years developing in the minor leagues, where he demonstrated his potential as a starting pitcher. Ujdur made his major league debut with the Tigers on September 7, 1980. During his initial stint with the team, he showed glimpses of his capabilities, although he spent much of his early career bouncing between the majors and minors.
Ujdur's most active season came in 1982 when he became a regular part of the Tigers' starting rotation. That year, he pitched in 30 games, starting 25 of them. He finished the season with a 10-10 win-loss record and an earned run average (ERA) of 3.69. Ujdur's performance in 1982 included two complete games and one shutout, showcasing his ability to handle a significant workload and deliver solid outings for the team.
Despite his efforts in 1982, Ujdur struggled to maintain a consistent presence in the major leagues in the following seasons. In 1983, he appeared in only 14 games for the Tigers, posting a 2-3 record with a 5.81 ERA. His time with Detroit came to an end after the 1983 season.
In 1984, Ujdur signed with the Cleveland Indians, hoping to revitalize his career. However, his tenure with the Indians was brief, as he pitched in only four games, all in relief, and recorded a 6.75 ERA. After his short stint with Cleveland, Ujdur's major league career concluded.
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