Originally signed by the St. Louis Cardinals in 1996, Ozuna spent two years in the Cardinal farm system before being traded with Braden Looper and Armando Almanza to the Florida Marlins for Édgar Rentería on December 14, 1998.
Ozuna would spend four years with the Marlins organization before being traded again. This time he was traded with Charles Johnson and Vic Darensbourg to the Colorado Rockies for Mike Hampton and Juan Pierre on November 16, 2002. In 48 games with Florida, Ozuna had 21 hits in 71 at bats for a .295 batting average.
Ozuna spent one year with the Colorado Rockies. In 17 games, he had 8 hits in 40 at bats for a .200 batting average. He was released on December 14, 2003.
Ozuna signed with the Chicago White Sox on January 19, 2005. He appeared in a career high 70 games and also had career highs with 203 at bats, 56 hits, and 11 RBI. Ozuna also had 14 stolen bases including a steal of home. He was brought back in 2006 and on May 3, 2006, he hit his first career home run, a solo shot, to tie the game with two outs in the 9th inning against Eddie Guardado of the Seattle Mariners.
On October 12, 2005, during Game 2 of the ALCS, A. J. Pierzynski advanced to first base on a controversial dropped third strike call. Ozuna pinch ran for him, stealing second base on the second pitch of the at bat to Joe Crede. Ozuna scored the game winning run on a double by Crede to end the controversial game. It was one of only two games Ozuna appeared in during the postseason as the White Sox won the World Series (the other being the night before).
On May 3, 2006, Ozuna hit a 2-out game tying home run in the bottom of the ninth, forcing the game into extra innings after a blown save by Cliff Politte. In the bottom of the 11th, Ozuna had another two out hit, a bouncer up the middle that he stretched into a double. His heads up play allowed Juan Uribe to bat in the winning run with a soft fly ball to short left center.
In 2007, Ozuna was injured in a game against Tampa leading off the 1st inning.
Ozuna was designated for assignment on July 8, 2008, and released on July 16.
On July 20, 2008, he signed with the Los Angeles Dodgers for the remainder of the season. On July 20, 2008, in his first game with the Dodgers, was put in as a pinch-runner for Andy LaRoche after he singled in a run to make it a one-run game against the Arizona Diamondbacks in the top of the ninth with two out. Matt Kemp then doubled him home, tying the game. The Dodgers eventually won the game, and tied with Arizona for first place in the N.L. West.
On September 19, 2008, he hit his 3rd career home run.
On January 15, 2009, Ozuna signed a minor league contract with an invitation to spring training with the Philadelphia Phillies, but began the season with the Phillies AAA minor league team, Lehigh Valley IronPigs. On June 11, he was suspended 50 games for violating the Major League Drug Prevention and Treatment Program. He was released on August 8, 2009.
On July 9, 2010 Ozuna signed a contract with the Newark Bears of the independent Atlantic League of Professional Baseball. He played in 28 games for the Bears, hitting .294.