Cueto (8-3) won his third straight start and first ever against the Mets, holding New York to six hits while walking one and striking out eight en route to the win.
Jose Arredondo got the final two outs of the seventh and Sean Marshall completed a four-out save, his ninth of the season, as the National League Central-leading Reds won their sixth straight overall.
Chris Young (1-1) absorbed the loss, surrendering three runs (two earned) on nine hits over seven full frames.
The Mets managed only five runs over the three-game series.
2014: The Year in Music [PHOTOS]