Jeff Parker played his youth hockey in the fertile environment of Minnesota. On his way up, he appeared to be a solid professional prospect as early as his days in high school. He was drafted 111th overall by the Buffalo Sabres in 1982 Entry Draft. At age 18, however, he elected to attend university first before contemplating a career with the pros.
From 1983 to 1986, the right winger studied by day and skated for the Michigan State Spartans of the CCHA at night. In his final season, he became a solid scorer and was selected to the NCAA Championship All-Tournament Team.
In 1986-87, Parker turned pro with the Buffalo Sabres. His role at the NHL level, however, was much more defensive in orientation than during his college days. Throughout the five seasons that followed, he struggled to win ice time with the Sabres on a consistent basis. Each year, he spent at least part of his season with the Rochester Americans of the AHL. It wasn't until 1989-90 that he earned his one and only complete campaign in the NHL. During that time, he struggled offensively as a fourth-line winger with a limited mandate to fill in gaps wherever needed.
In 1990, Parker was traded to the Winnipeg Jets. Shortly thereafter, he signed as a free agent with the Pittsburgh Penguins who then traded him to the Hartford Whalers in March of 1991. In Connecticut, the well-traveled winger appeared in only four contests before deciding to hang his blades up for good.