Jarrod Saltalamacchia cracked a solo homer among his two hits and scored twice for Miami, which was won four straight games. Tom Koehler (3-2) allowed three hits and two walks over seven scoreless innings to notch the win.
Josh Beckett (0-1) faced his former club for just the second time in his career. He surrendered four runs on eight hits and a walk over 6 2/3 frames for the Dodgers, who had their three-game winning streak snapped.
The 33-year-old Beckett was the second overall pick of the 1999 draft by the Florida Marlins and debuted with them in 2001. He spent five seasons with the franchise, with the highlight of his tenure coming in 2003, when he was named the World Series MVP during their second championship in club history.
The Marlins held a 2-0 lead after six innings, but put the game away following a four-run seventh.
Jones led off the frame with a double and after Marcell Ozuna struck out and Adeiny Hechavarria grounded out, pinch-hitter Reed Johnson slapped a single into right-center to bring home Jones.
Christian Yelich then ripped a triple into the gap in left-center to plate Johnson and after Derek Dietrich was hit by a pitch, Giancarlo Stanton stepped up next and squirted a grounder back up the middle to score Johnson. Casey McGehee's base hit into right brought home Dietrich to make it 6-0.
The Dodgers got a pair of runs back in the eighth on RBI singles by Dee Gordon and Yasiel Puig off Carlos Marmol, but Steve Cishek allowed just an RBI groundout to Carl Crawford after Miguel Olivo tripled in the ninth to seal the outcome.
Earlier, Saltalamacchia's one-out solo shot to right in the second opened the scoring and Jones' RBI double in the fourth gave the Marlins their 2-0 spread.