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. The right-hander 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.
Tim Hudson (2-1) 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.