Brian McCann homered and the Braves scored four runs in the third inning.
Cueto (4-1) led the major leagues with his 1.12 ERA before giving up six runs, five earned, on eight hits in four innings.
He had allowed only one earned run over 23 innings in his last three starts.
The first-place Braves moved one-half game ahead of the Nationals in the NL East.
Atlanta got a strong outing from Tim Hudson (2-1). He threw six scoreless innings before giving up two runs in the seventh. He allowed nine hits and two runs in seven innings.
Michael Bourn had three hits and scored two runs and Martin Prado also had three hits for the Braves.
Kris Medlen gave up two hits in the eighth before ending the inning on pinch-hitter Ryan Ludwick’s flyball to left field.
Craig Kimbrel gave up two-out walks to Joey Votto and Brandon Phillips in the ninth before closing out the win on Jay Bruce’s groundout.
Cueto’s ERA rose to 1.89, leaving Atlanta’s Brandon Beachy (1.60) with the majors’ best mark.
McCann hit his sixth homer, his first since May 2, in the second inning.
The Braves sent 11 batters to the plate while scoring four runs off Cueto in the third.
Prado and Chipper Jones had run-scoring singles, Jason Heyward doubled in a run and Dan Uggla added a sacrifice fly in the long inning.
The Reds committed two errors to help the Braves score an unearned run in the fourth.
Bourn singled and moved to second on Cueto’s wild pickoff attempt. A fielding error by Chris Heisey in left field on Prado’s single allowed Bourn to score for a 6-0 lead.
Ryan Hanigan’s double drove in Todd Frazier for the Reds’ first run in the seventh. Drew Stubbs’ single drove in Hanigan.