Fernandez (3-1) outpitched Atlanta's Alex Wood (2-3), who also was dominant. Wood allowed four hits and one run with no walks and a career-high 11 strikeouts in eight innings.
The Marlins gave Fernandez the only run he would need in the fourth. Giancarlo Stanton hit a one-out double to left field and scored on Casey McGehee's single up the middle.
Fernandez struck out the side in the fourth and fifth innings. He allowed three hits with no walks.
Cishek pitched a perfect ninth for his fourth save.
Jason Heyward led off the first with a single to left field, and the Braves didn't have another hit until Chris Johnson's leadoff single in the eighth. Fernandez then struck out Dan Uggla and Evan Gattis before Andrelton Simmons' infield single moved pinch-runner Tyler Pastornicky to second.
Pinch-hitter Ryan Doumit grounded out to Fernandez to end the eighth.
Atlanta's only other baserunner before the eighth came when B.J. Upton reached on McGehee's fielding error at third base in the fourth. Fernandez then struck out the next two batters to end the inning.
It was the second straight start Fernandez did not allow an earned run. He allowed three unearned runs and received no decision in the Marlins' 6-3 loss to Washington on April 16.
Fernandez set his career high with 14 strikeouts against Cleveland on Aug. 2, 2013. Wood's previous high was nine strikeouts against Washington on Aug. 16, 2013.
Wood lowered his ERA from 1.67 to 1.54 in the loss.
The game lasted 2 hours, 8 minutes.
NOTES: Braves LHP Mike Minor (sore left shoulder) will make one final minor league rehab with Double-A Mississippi at Pensacola on Friday. Minor had been tentatively set to make his 2014 Atlanta debut on Saturday before being pushed back. ... Christian Yelich, who led off the game with a bunt single, has a 16-game hitting streak. ... The Braves traded Triple-A Gwinnett IF Tyler Greene to San Diego for a player to be named later. Greene will be assigned to the Padres' Triple-A El Paso team. ... Atlanta RHP Aaron Harang will face Miami RHP Nathan Eovaldi on Wednesday.