Jeff Shaw's journey in Major League Baseball began when he was drafted by the Cleveland Indians in the first round of the 1986 MLB Draft. A right-handed pitcher, Shaw made his MLB debut with the Indians in 1990. Over the next few years, he worked to establish himself as a reliable pitcher, though his early career was marked by transitions between starting and relieving roles.

In 1992, Shaw was traded to the Montreal Expos, where he continued to develop his skills on the mound. His time with the Expos was relatively short, and by 1995, he found himself with the Chicago White Sox. However, it was his move to the Cincinnati Reds in 1996 that marked a turning point in his career. With the Reds, Shaw transitioned into a full-time relief pitcher, eventually becoming the team's closer.

Shaw's performance as a closer for the Reds was impressive. In 1997, he recorded 42 saves, earning him a spot in the All-Star Game. His ability to consistently close out games made him a valuable asset to the Reds' bullpen. The following year, Shaw continued to excel, and his efforts were recognized once again with another All-Star selection.

Midway through the 1998 season, Shaw was traded to the Los Angeles Dodgers in a high-profile deal. Despite the mid-season transition, he maintained his effectiveness as a closer, finishing the year with a combined total of 48 saves between the two teams. Shaw's tenure with the Dodgers solidified his reputation as one of the league's reliable closers.

Shaw continued to serve as the Dodgers' closer through the 2001 season. During his time in Los Angeles, he consistently delivered strong performances, providing stability to the team's bullpen. His ability to handle high-pressure situations and close out games was a testament to his skill and experience on the mound.

After the 2001 season, Shaw decided to retire from professional baseball. Over the course of his career, he accumulated 203 saves and maintained a solid earned run average, reflecting his effectiveness as a relief pitcher. Shaw's career was characterized by his adaptability and his ability to perform under pressure, making him a respected figure among his peers and fans alike.