Tyler Pastornicky greeted Dodgers closer Javy Guerra (1-2) with a leadoff single in the ninth and advanced on a sacrifice by pinch-hitter Jack Wilson. Michael Bourn struck out, but Prado drove a 1-2 pitch to center field and over the head of two-time Gold Glove winner Matt Kemp, who caught up to it in the warning track but couldn't hold onto the ball.
Eric O'Flaherty (1-0) pitched 1 1-3 hitless innings for the victory and Craig Kimbrel worked a scoreless ninth for his sixth save in as many attempts.
Jones, playing in his 19th and final big league season, was 1 for 3 with a walk in what could have been his last game at Dodger Stadium if the predictions of rain for Wednesday's series prove accurate. After the third inning, the left field video board flashed the message: "Happy birthday Chipper. The Dodgers salute your remarkable career," while organist Nancy Bea Hefley played "Think Of Me" from the musical "Phantom of the Opera."
The seven-time All-Star, whose 457 career homers are the third-most among switch-hitters behind Mickey Mantle and Eddie Murray, hit a towering drive into the Atlanta bullpen in right field on Aaron Harang's first pitch of the fifth to put the Braves on the board. They tied it 2-all five batters later on a bases-loaded groundout by Martin Prado.
Jones came up again in the sixth with two on and none out. Dodgers manager Don Mattingly went to the mound for a chat with Harang and decided to leave the right-hander in to pitch to Jones, whose comebacker was turned into a double play.
Harang intentionally walked Jason Heyward before Brian McCann scored on a wild pitch, giving the Braves a 3-2 lead, but the Dodgers tied it in the bottom half. Dee Gordon scored from second when second baseman Dan Uggla's relay throw in the dirt on a potential double-play grounder by Matt Kemp couldn't be handled by first baseman Freddie Freeman.
Juan Rivera gave Los Angeles a 2-0 lead in the first with a two-out drive against lefty Mike Minor that curved around the left field pole after a single by Mark Ellis. Rivera became the 20th player to homer into the Loge deck at Chavez Ravine and the eighth to do it with the Dodgers. The first was Frank Howard in Game 4 of the 1963 World Series against the Yankees' Whitey Ford.
Harang allowed three runs, six hits and four walks over six innings. Minor gave up three runs, eight hits and no walks through six.
Notes: Jones has homered on his birthday four times since coming up to the big leagues in 1993, including his 24th, 29th (twice) and 36th. He has played on his birthday 13 times, going 21 for 49, and the Braves are 11-2 in those games. ... Rivera left the game with a strained left hamstring after getting an infield single off Minor's leg in the sixth. ... Los Angeles placed RHP Matt Guerrier on the 15-day DL, retroactive to April 19, because of tendinitis in his elbow and recalled LHP Michael Antonini from Triple-A Albuquerque. ... The Braves recalled RHP Cory Gearrin from Triple-A Gwinnett to fill the roster spot left vacant when RHP Jair Jurrjens was demoted to Gwinnett following his loss on Monday night. ... The Dodgers have outscored their opponents 19-5 in the first inning. ... Jones' homer was his 13th at Dodger Stadium.