Jones, who had three RBI, singled in the first inning to extend his hitting streak to 16 games, and then homered as part of a six-run outburst in the fourth inning. The extra-base hit tied a mark set by Pittsburgh's Paul Waner in 1927.
Brian McCann homered for a second straight game and drove in three runs for the Braves, who have won five straight and nine of their last 11 games.
Scott Thorman added a two-run double and left-hander Chuck James (4-0) remained unbeaten in his major league career after allowing six hits and five runs in five innings.
San Diego starter Jake Peavy (4-9) gave up nine hits and seven runs over six innings in his fourth straight loss. Peavy hasn't won since May 28.
Khalil Greene had a two-run homer for the Padres.
San Diego Manager Bruce Bochy and bench coach Tony Muser were ejected in the top of the sixth inning, and Atlanta Manager Bobby Cox and right-fielder Jeff Francoeur were tossed in the top of the seventh.
Swim Week Miami Beach 2014 [PHOTOS]