Swanson was awarded $10 million rather than the team's $9.2 million offer by Jeanne Charles, Richard McNeill and Scott Buchheit, who heard arguments Tuesday.
Duvall was given the Braves' $9,275,000 offer rather than his $10,275,000 request by Gary Kendellen, Keith Greenberg and Gil Vernon, who listened to arguments Friday.
Swanson, 28, hit .248 last year, when he set career highs with 27 homers and 88 RBIs. He had a pair of homers and three RBIs in the World Series against Houston, helping the Braves win their first title since 1995.
Swanson made $6 million last season and is eligible for free agency after the World Series. He entered Wednesday with a .279 average, six homers and 26 RBIs.
Duvall led the NL with 113 RBIs last year for Miami and Atlanta, which acquired him on July 30. The 33-year-old hit .228 with 38 home runs during the season and had two homers and six RBIs in the World Series. He also is eligible for free agency after this season and is hitting .199 with three homers and 18 RBIs this year.
No statistics or evidence from after March 1 are admissible other than contract and salary comparisons. The timing was set when Major League Baseball and the players' association agreed to the deal that ended the lockout.
Seattle second baseman/outfielder Adam Frazier ($8 million) and Kansas City outfielder Andrew Benintendi ($8.5 million) also won their cases earlier. St. Louis outfielder Tyler O'Neill ($3.4 million), Miami right-hander Pablo López ($2.45 million) and Milwaukee right-hander Adrian Houser ($2.425 million) lost.
Arbitration hearings usually are held during the first three weeks of February, but they were delayed by the lockout.
Hearings are scheduled through June 24. Other players still scheduled for hearings include New York Yankees outfielder Aaron Judge, Chicago Cubs catcher Willson Contreras, Minnesota catcher Gary Sánchez, Miami catcher Jacob Stallings, Seattle outfielder Jesse Winker, Kansas City second baseman Nicky Lopez and Cincinnati pitcher Lucas Sims.