Sheets (1-0), the former ace of the Milwaukee Brewers, made his first major league appearance since July 10, 2010, and dazzled New York, issuing one walk and striking out five.
The right-handed four-time all-star signed a minor-league contract with the Braves July 1 in a bid for a comeback following elbow surgery. He was promoted last week after making two rehab starts for Class AA Mississippi.
The Braves backed him with a six-run outburst in the fifth inning, capped by Freddie Freeman's three-run homer as Atlanta completed a three-game sweep of the Mets and logged their seventh straight victory overall.
New York's Johan Santana (6-6) absorbed the loss, allowing six runs on eight hits over five full innings.
Andres Torres went 2-for-4 with an RBI single for the Mets.