Wheeler (1-0), a former first-round draft pick obtained by New York from San Francisco in 2011, overcame five walks and four hits to blank the Braves in a 102-pitch performance.
The 23-year-old right-hander struck out seven for the Mets, who bested the National League East-leading Braves 4-3 in the rain-delayed first game earlier Tuesday.
Anthony Recker broke a scoreless tie with a two-run homer in the seventh and Omar Quintanilla helped seal the triumph with a two-run single in the eighth.
Atlanta's Paul Maholm (7-6) was tagged with the loss despite surrendering just two runs on nine hits over seven full frames.
Justin Upton corralled the Braves' only RBI.