Prior to his professional career, Moore played for the Harvard Crimson in the Eastern College Athletic Conference, along with his two brothers, Mark and Steve Moore. In 1999–00, Dominic joined both older brothers on the Crimson team, marking the first-ever brother trio in school history to play at the same time. Moore is currently ranked eleventh in all-time scoring at Harvard, and is ranked tenth on the school's all-time goal-scoring list.
Moore was drafted in the third round, 95th overall, in the 2000 NHL Entry Draft by the New York Rangers. Moore began his professional career in the 2003–04 NHL season, in which he split time between the Rangers and their minor league affiliate, the Hartford Wolf Pack of the American Hockey League. Moore made his NHL debut on November 1, 2003, against the Montreal Canadiens, where he tallied three assists in a 5–1 victory. He became the second Ranger ever to score three points in his NHL debut, joining George Allen, who did so in 1938. During the NHL lockout of the 2004-05 season, Moore remained with the Wolf Pack and finished third on the team in scoring for the year.
Moore rejoined the Rangers at the start of the 2005–06 NHL season, where he was placed on a defensive-minded line with Jed Ortmeyer and Ryan Hollweg. Through minor line-changes throughout the year, Moore had continued his solid defensive play and continued to improve.
On July 19, 2006 the Rangers traded Moore to the Pittsburgh Penguins in a three team trade. Moore would play part of one season with the Penguins, playing in 59 games and scoring 6 goals and 15 points. Midway through the 2006-07 season, Moore was traded to the Minnesota Wild for a third round draft pick. Moore went on to play in 40 games for the Wild over parts of two seasons with the club, scoring 3 goals and 5 points in that time.
On January 11, 2008, the Maple Leafs claimed Moore off waivers from the Wild. He made his debut with the Maple Leafs on January 12, 2008 against the San Jose Sharks. In a partial season with the Maple Leafs, Moore had 4 goals and 14 points in 38 games. Moore began the 2008-09 season with the Maple Leafs, and has been one of the team's more consistent two-way forwards. As of December 2008, Moore was on pace to break his career high season totals of goals, assists, and points.