Fernandez allowed only one earned run in six innings and the Miami Marlins won 6-2 Monday, giving Los Angeles consecutive losses for the first time since June 20-21.
Puig went 0 for 3 against Fernandez in the first matchup between the Cubans.
Logan Morrison doubled home a run in the seventh to put Miami ahead to stay. Giancarlo Stanton added his 15th homer in the eighth, when Miami scored three times against a bullpen that has been the best in the majors over the past month.
Three Marlins relievers followed Fernandez (9-5) completed the six-hitter.
The Dodgers fell to 25-5 since the All-Star break and lost for only the third time in their past 22 road games. They had a 10-game winning streak snapped Sunday at Philadelphia.
Hyun-Jin Ryu (12-4) lost for the first time in his eight starts.
Source: Associated Press