The Marlins improved to 5-1, their best start since 2009. Last year their fifth victory came in their 21st game, and they finished with 100 losses.
Fernandez (2-0) improved his career record at home to 11-0 even though he was at less than his best. He allowed his first two walks of the season back to back. His foot slipped on a delivery, and the pitch bounced several feet in front of the plate. One frustrating inning ended with the Marlins' ace shaking his head and screaming angrily into his glove.
Fittingly, he left the game after throwing a wild pitch on a strikeout that allowed Alexi Amarista to reach base.
But Fernandez allowed only three hits, walked two and struck out eight. Three relievers followed to complete a five-hitter.
Andrew Cashner (0-1) allowed only two runs in six innings, but the offensively challenged Padres reached a new low - for the first time, they were shut out. They've scored eight runs this season, worst in the majors, and have lost four in a row since a win on opening day.
The Padres went 0 for 7 with runners in scoring position and are batting .108 (4 for 37) in those situations.
San Diego's best threat against Fernandez came when he walked two to load the bases with the score 0-0 in the third, but he escaped when Seth Smith hit into an inning-ending double play.
The game drew a crowd of 35,188, including Miami Heat owner Micky Arison and president Pat Riley, who chatted briefly with Marlins owner Jeffrey Loria.
Stanton's run-scoring single in the third put the Marlins ahead 1-0. Derek Dietrich made it 2-0 in the sixth with an RBI single, and Stanton doubled home a run in the seventh.
Miami's Adeiny Hechavarria, who began the day leading the NL in batting, went 0 for 5 to drop his average to .458.
Notes: Marlins 2B Rafael Furcal (hamstring) is scheduled to report Monday to extended spring training in Jupiter, Fla., with rehabilitation assignments to follow. He likely won't be activated until April 20 at the earliest. ... Padres RHP Casey Kelly was scheduled to pitch in a simulated game Saturday, but the workout was postponed at least two days because he was feeling discomfort in his surgically repaired elbow, manager Bud Black said. The setback isn't believed to be significant. ... Padres RHP Tyson Ross will get an extra day of rest before his next start Tuesday at Cleveland. Black said he made the move in part so the two left-handers in the rotation wouldn't pitch back to back. ... Stanton has two homers in eight at-bats against RHP Ian Kennedy (0-1, 5.40), who is scheduled to start Sunday for the Padres. RHP Nathan Eovaldi (1-0, 3.00) will start for Miami.