Cueto (15-6) allowed only one runner as far as third base in the dominating performance, during which he scattered three hits, issued a pair of walks and struck out three.
The right-hander won for the sixth time in seven starts while lowering his ERA to 2.45, third-best in the National League.
Jay Bruce clouted a two-run homer and Ryan Ludwick added a solo shot for the National League Central-leading Reds, who improved to an MLB best 22-8 since the All-Star Game break.
Chicago rookie Brooks Raley (0-2) fell in the second major-league start, yielding three runs on five hits over six innings.
2014: The Year in Music [PHOTOS]