Jones hit his first blast in the opening inning, but the Dodgers overcame an early three-run deficit and took a 4-3 lead in the fourth.
The Pirates then tied it in the bottom half of the fourth and moved in front to stay in the fifth on Jones' second three-run shot of the game. Both of the homers came off starter Joe Blanton (8-11), who also allowed a solo shot to Pedro Alvarez in the fifth before being lifted.
Blanton has yet to win in three starts since the Dodgers acquired him from Philadelphia Aug. 3.
Pittsburgh had lost nine straight meetings with the Dodgers.
The win went to A.J. Burnett (15-4) even though he gave up six runs on seven hits in 6 2/3. He became the first 15-game winner for the Pirates in 13 years.
Clint Barmes drove in three Pittsburgh runs, one with a triple in the fourth and two with a single in the seventh.
2014: The Year in Music [PHOTOS]