[1] Paek played in the National Hockey League (NHL) from 1990–91 to 1994–95, and won the Stanley Cup twice, in 1991 and 1992 with the Pittsburgh Penguins.

After four seasons and two Stanley Cups in Pittsburgh, Paek was traded mid-season to the Los Angeles Kings in 1993–94 as part of the deal that brought Tomas Sandström to the Penguins.

With the exception of 40 games in 2001–02 with the Anchorage Aces of the West Coast Hockey League, he played out the rest of his career with the Panthers, retiring after the 2002–03 season.

In 2004, Paek served as an assistant coach for the St. Edward High School, leading the team to an Ohio state championship.

While coaching at St. Edward, he also served as a co-coach of the Cleveland Panthers bantam minor squad, leading them to an Eastern Elite Amateur Hockey League title.

On 11 August 2005, Paek was named the assistant head coach for the Grand Rapids Griffins of the American Hockey League (AHL).