Blevins was 5-0 with a 3.15 ERA in a career-high 67 games this year and has a 13-6 record with a 3.30 ERA in 281 big league games over seven seasons, all with the Athletics. He's averaged 8.1 strikeouts per nine innings.
The 24-year-old Burns hit .315 with 37 RBIs and 74 steals this year for Class A Potomac and Double-A Harrisburg. He was selected Washington's minor league player of the year.
The trade was announced Wednesday at the winter meetings.