Cueto (16-6) allowed a pair of runs on only three hits, didn't issue a walk and struck eight while tossing 74 of his 107 pitches for strikes.
The Reds ace won for the seventh time in eight starts and lowered his ERA to 2.44, second-best in the National League behind Washington's Jordan Zimmerman.
Todd Frazier went 2-for-3 with a solo homer and two RBI while Xavier Paul connected for a two-run blast and Miguel Cairo added a bases-empty shot for the NL Central-leading Reds, who won for the seventh time in eight games.
Chicago's Jeff Samardzija (8-11) was tagged with the loss, allowing four runs on six hits over five full innings.
Alfonso Soriano belted a two-run homer for the Cubs.