Jones homered in the second and fourth innings off Mets starter Pedro Astacio, extending his string of consecutive at-bats with a home run to four. He hit two Saturday against Montreal before being hit in the head with a pitch.
The Braves' center fielder became the 11th National Leaguer to homer in four straight at-bats and the second in franchise history, joining Bobby Lowe, who did it for the Boston Beaneaters in 1894.
Hall of Famers Mike Schmidt and Ralph Kiner did it twice.
Matt Franco had the big blow in a pinch hitting role against his former team - a bases-clearing triple that gave Atlanta an 11-6 lead in the fifth. The Braves trailed 5-0 before they came to bat in the second.
Astacio (12-9) allowed eight runs and eight hits in four-plus innings, then was ejected after hitting Gary Sheffield with a pitch. Mets right fielder Joe McEwing had been hit by rookie Trey Hodges in the top of the fifth.
Hodges (1-0) earned his first major league win, allowing one run in three innings of relief.
Braves rookie Damian Moss was tagged for five runs and eight hits in the first two innings.