The award honors the player who best represents the ideals of sportsmanship on the court.
Allen, acquired from the Milwaukee Bucks on Feb. 20, is the second Sonic to win the award, joining Hersey Hawkins, who earned the honor following the 1998-99 season.
Allen received 519 points, including 38 of a possible 116 first-place votes, from a panel of sportswriters and broadcasters throughout the United States and Canada.
The three-time NBA All-Star was one of four divisional finalists that included New York guard Allan Houston from the Atlantic, New Orleans forward P.J. Brown from the Central, and Dallas guard Michael Finley from the Midwest.
Houston finished second with 485 points, followed by Brown (480) and Finley (372.)
The award is named for former Detroit Pistons guard Joe Dumars, the original recipient following the 1995-96 campaign.
The NBA will donate $25,000 on Allen's behalf to his Ray of Hope Foundation.