He played in the National Hockey League (NHL) with the Ottawa Senators, Carolina Hurricanes, Detroit Red Wings, Nashville Predators, Dallas Stars and Anaheim Ducks.

Also during that time he represented his country at the 2004 World Junior Ice Hockey Championships, tallied one goal and five assists in six games.

On February 11, 2008, the Senators traded Eaves along with Joe Corvo to the Carolina Hurricanes in exchange for Cory Stillman and Mike Commodore.

On July 24, 2009, Eaves was traded by the Hurricanes to the Boston Bruins along with a 2010 fourth-round draft pick in exchange for defenseman Aaron Ward.

Predators defenceman Roman Josi's shot hit him in the side of the face; Eaves missed the rest of the season due to the concussion.

[10] On March 5, 2014, Eaves was traded to the Nashville Predators, along with Calle Järnkrok, as part of a deal that brought David Legwand to Detroit.

[13] In the midst of the 2016–17 season, his third and final year of contract with the Stars, Eaves had already established career highs with 21 goals and 37 points, playing on the top offensive line, alongside Jamie Benn and Tyler Seguin.

On June 23, 2017, Eaves opted to give up his impending free agent status to sign a three-year, $9.45 million contract to remain with the Ducks.

Eaves met his wife Katie in Chicago in 2007 while driving home to Minnesota after his Ottawa Senators lost the 2007 Stanley Cup Finals.

[19] On October 23, 2017, after experiencing trouble breathing and weakness in his legs, Eaves was initially diagnosed with Guillain–Barré syndrome, an autoimmune nervous disorder.