It was quite a turnaround from Sunday, when the Braves committed four errors, issued eight walks and lost to Washington 15-6.
"Yesterday those Little Leaguers from Columbus who won the World Series could have beat us," Jones said. "Today was as solid a game as we have played from first pitch to the end of the ninth inning."
Campillo (5-4) retired the first 12 batters, and he and two relievers combined to retire the final nine Marlins. Mark Teixeira and Mark Kotsay each had two hits, drove in a run and scored once, and shortstop Brent Lillibridge twice robbed Florida of hits.
"We need to do something on this trip and get it going, and tonight was a great start," manager Bobby Cox said.
Amid such a polished performance, Jones' brain cramp stood out. He lost track of the count in his fourth at-bat and started up the baseline after ball three.
"I'm just glad I didn't get all the way to first," Jones said with a sheepish grin. "Then I swung at ball four and ball five after that."
Jones struck out to finish 1-for-4, dropping his average to .556 (20-for-36) against Florida this year.
The 29-year-old Campillo, who moved into the rotation in May, walked one and lowered his ERA to 2.83. His effort was a welcome turnaround for the Braves, who had given up 23 runs and 31 hits in their past two games, both losses.
"He has been that good all year long," Cox said. "Nobody really swung well at him, which is normal. He does that all the time."
The Marlins lead the majors with 140 home runs, but they're a fastball-hitting team, and Campillo rarely topped 80 mph. It was reminiscent of the Marlins' loss Friday to junkballer Jamie Moyer of Philadelphia, who has beaten Florida 10 times in 10 career starts.
"He was like a right-handed Jamie Moyer, except his fastball was a little better," said Jeremy Hermida, who had one of Florida's two hits. "He hit the corners with all of his pitches, and that's difficult to do."
Florida's Chris Volstad (2-1) allowed three runs in six innings in his third major league appearance for the Marlins, who fell a game behind the idle NL East leaders, Philadelphia and the New York Mets.
"We didn't put anything together," Jacobs said. "He just throws a lot of stuff, mixing his pitches up, and we weren't able to get anything going."
Hermida singled leading off the seventh for the Marlins' other hit.
"I know those guys are really dangerous," Campillo said. "But I felt really good."
Lillibridge's glove work erased two potential singles. He ranged to his left to snare a grounder and spun to throw out a href="http://sports.espn.go.com/mlb/players/profile?playerId=29183">John Baker in the third, and made a diving stop of a grounder hit by pinch hitter Robert Andino in the sixth.
Atlanta took a 1-0 lead in the second on Kotsay's bases-loaded single with none out, but Volstad escaped further damage. Lillibridge and Campillo tapped into forceouts at the plate, and Gregor Blanco struck out.
Blanco walked in the fifth, stole second and came home on a two-out single by Chipper Jones. Teixeira followed with an RBI double to make it 3-0.
Pinch hitter Martin Prado doubled home a run in the ninth.
After the game, the Marlins said RHP Rick VandenHurk will be recalled from Double-A Carolina to start Tuesday. RHP Jesus Delgado was optioned to Carolina. ... Atlanta SS Yunel Escobar (sore left shoulder) is expected to rejoin the lineup Tuesday, Cox said. ... Baker's bat sailed about 150 feet into the stands when it slipped from his hands as he struck out swinging in the eighth.