Duda was born in Fontana, California, on February 3, 1986 to David and Eleanor Duda. He attended Arlington High School in Riverside, California. Duda then enrolled in the University of Southern California (USC), where he played college baseball for the USC Trojans baseball team from 2005 through 2007. Duda played 143 games for the Trojans, hitting 11 home runs, with 81 runs batted in, and a .275 batting average.

Duda was selected by the New York Mets in the seventh round of the 2007 Major League Baseball draft, as the 243rd overall selection. He began his professional career in 2007 with the Single-A Brooklyn Cyclones of the Short Season Single-A New York–Penn League, where he batted .299, with 32 runs batted in, 32 runs, and 4 home runs. During the following winter, he played on the Waikiki BeachBoys of Hawaii Winter Baseball, batting .340, with 13 runs batted in, 12 runs, and 3 home runs. In 2008, he played for the St. Lucie Mets of the Single-A Florida State League, where he batted .263, with 66 runs batted in, 58 runs, 11 home runs. For the 2009 season, Duda was promoted to the Double-A Binghamton Mets, where he batted .281, with 53 runs batted in, 49 runs, and 9 home runs. During the fall of 2009, Duda played for the Surprise Saguaros of the Arizona Fall League, where he in 5 at bats batted .400, with 2 runs batted in and no home runs.

On August 31, 2010, the Mets announced that Duda would be added to the major league roster as part of their September call-ups. Duda made his major league debut on September 1, against the Atlanta Braves, facing starting pitcher Tommy Hanson, whom he played against in high school. He went hitless in three at-bats, but made a “stellar sliding catch” in the outfield. Duda had to leave the game in the eighth inning due to hamstring cramps, which he said came from dehydrating while on the plane from Buffalo to Atlanta. On September 17, 2010, again batting against Hanson, Duda hit his first career major-league home run. Former Mets manager Jerry Manuel watched Duda during batting practice when he was first called up to the Majors and noted that Duda reminded him of Magglio Ordóñez or Moisés Alou.

With Ike Davis starting at first base, Duda’s primary position in the minor leagues, all of Duda’s playing time came in left field. He batted .202 for the year. The Mets named Duda their Sterling Organizational Player of the Year in 2010.

On April 10, 2011, Duda was optioned to the Triple-A Buffalo Bisons.

On August 8, 2011, batting in the cleanup spot for the first time in his major league career, Duda picked up his first major-league walk-off hit, with a two-run single off of Padres closer and former Mets reliever Heath Bell. He batted .292 for the season.

Duda was selected as the starting right fielder for the Mets to begin the 2012 campaign. On April 7, 2012, Duda had his first multi-homer game, hitting two solo shots off the Atlanta Braves in a 4–2 Mets’ victory. Going into June 26, Duda was hitting .269 with a team-high 11 home runs, yet from June 26 to July 24 Duda was hitting .138 with one home run and a .200 slugging percentage. The sub par batting performance coupled with poor fielding prompted his being demoted to Triple-A Buffalo.

In November, Duda represented Major League Baseball in the 2014 Major League Baseball Japan All-Star Series. He went 4-for-10 with two walks in the exhibition series.

In the fourth game of the 2015 NLCS, Duda batted in five runs to help the Mets sweep the Chicago Cubs and advance to the 2015 World Series. His five RBI was tied for the most by a Mets player in a single postseason game, a feat previously accomplished by Curtis Granderson in the 2015 NLDS, Carlos Delgado in the 2006 NLCS, Edgardo Alfonzo in the 1999 NLCS and Rusty Staub in the 1973 World Series.

On January 12, 2016, the Mets re-signed Duda to a 1-year contract. On May 23, the Mets placed Duda on the 15-day disabled list with a stress fracture in his lower back. He was replaced on the roster by Ty Kelly. Duda was batting .231 with a .297 OBP and .431 SLG with seven HR and 19 RBIs in 39 games.

On July 27, 2017, Duda was traded to the Tampa Bay Rays for minor league pitcher Drew Smith. He batted .175 for Tampa Bay. He became a free agent after the season.

Duda signed a one-year contract with the Kansas City Royals on February 28, 2018. In his first at-bat as a Royal, he hit a three-run home run on Opening Day in the first inning against James Shields. Duda was the Royals’ designated hitter for the first half of the season, hitting .242 with 13 home runs and 48 runs batted in.

The Atlanta Braves acquired Duda and cash considerations from the Royals in exchange for a player to be named later or cash considerations on August 28, 2018.

On February 9, 2019, Duda signed a minor-league contract with the Minnesota Twins that included an invitation to spring training. Duda was released by the Twins on March 20, 2019.

On March 22, 2019, Duda signed a minor-league contract with the Kansas City Royals. He was placed on the injured list on April 26 with a lumbar strain injury. He was designated for assignment on July 27, 2019 after hitting .171 in 119 appearances. He was then released outright on the next day.

On August 5, 2019, Duda signed a minor league deal with the Atlanta Braves. The team released Duda on August 27, 2019.