Cueto (9-6) allowed two runs on six hits, striking out four and walking one. The right-hander bounced back from a setback in his last outing to win for the fourth time in five decisions.
Chris Heisey had three hits and Jay Bruce added a two-run homer for the Reds, who have won three straight, including the first two of this rare five-game set. Billy Hamilton contributed two hits and stole a pair of bases for Cincinnati, which has won four of five overall.
The Reds got to Chicago starter Travis Wood in the first inning with three runs and that's all Cueto and company needed.
Cueto cruised through the first inning and then his offense took over. Hamilton led off with a bunt single, stole second and scored on Brandon Phillips' RBI base hit. Bruce then followed with a blast to right for a 3-0 lead.
Wood settled down after the tough first inning, yielding just two hits through the next four innings.
Coghlan and Sweeney broke the scoreboard for the Cubs, as they led off the sixth with consecutive homers off Cueto. The hits ended a string of seven straight batters set down by Cueto, who had allowed just one hit through the first five frames.
The Reds, though, got a run back in the home half of the inning on a Ramon Santiago RBI base hit that also forced Wood from the contest.
Wood (7-7) was tagged with the loss, allowing four runs -- three earned -- on eight hits in 5 1/3 innings. He struck out five and walked two, falling to 0-2 over his last four starts.
Chicago threatened in the seventh, loading the bases with two outs, but Manny Parra came on for Cueto and struck out Coghlan, then got Sweeney to ground out to end the inning.
Jumbo Diaz came on to pitch a perfect eighth and Aroldis Chapman tossed the ninth for his 18th save of the season.
Celebrity Families of 2014 [PHOTOS]