It was the fifth complete game in Cueto's five-year career. Three of the route-going performances came last year when he compiled a 9-5 record in 24 starts.
Cueto (4-0) struck out four and did not walk a batter while throwing 110 pitches.
Kevin Correia (1-2) was charged with the loss after giving up five runs on nine hits in seven innings.
The Reds have won back-to-back games and the Pirates have dropped three out of four.