Hampton (9-5) allowed a run and five hits while walking one and striking out four, throwing 79 of 105 pitches for strikes on the way to his first complete game since July 23, 2001 against San Francisco.
The veteran lefthander had a no-hitter through 4 2/3 innings before Eddie Perez, a former Brave, singled to right field. Hampton faced just two over the minimum before allowing consecutive doubles in the seventh.
Vinny Castilla had a two-run triple in the second and a solo home run, and Hampton added a pair of RBI for the Braves, who took the final two games of the series by a combined score of 17-3 after dropping the opener, 4-3, on Tuesday.
Rookie Wes Obermueller (0-3) remained winless in the major leagues, surrendering seven runs in 4 1/3 innings.
2014: The Year in Music [PHOTOS]