Cueto (8-4) struck out eight, walked four and allowed only a lead-off, infield single to Felipe Lopez in the third.
Arizona's other hit was a bunt single by Gerardo Parra to open the seventh off Arthur Rhodes.
David Weathers and Francisco Cordero each worked a perfect inning, with Cordero earning his 19th save.
The hard-luck loser was Jon Garland (4-8), who allowed a run on six hits in six innings. He has not won a start since May 19, going 0-6 in eight outings since then.
The game's lone run came in the sixth, when Chris Dickerson singled, moved to second on a ground out by Jerry Hairston and scored on Joey Votto's single.
Copyright 2009 by United Press International.