Cueto, coming off an injury-plagued season, allowed two hits and struck out two. It was a big improvement over his second spring start, when he gave up six runs and seven hits to Kansas City in 2 2/3 innings.
"He was terrific," Reds manager Bryan Price said. "He made a lot of good, consistent pitches. He held the ball and varied his times to the plate."
A 19-game winner in 2012, Cueto struggled with a strained muscle on the right side of his back last year and was sidelined for 2 1/2 months. He finished 5-2 with a 2.82 ERA in 11 starts.
Angels left-hander Tyler Skaggs also threw four shutout innings, allowing one hit and two walks with three strikeouts.
Skaggs was better than his prior start as well. He yielded two runs and three hits in 2 1/3 innings against Texas.
"You couldn't ask for anything more," Angels manager Mike Scioscia said. "His stuff is (legitimate)."
Erick Aybar singled and stole second to start the fifth against Reds reliever Sam LeCure. Hank Conger followed with a single to score Aybar, and Conger went to second on the throw home. He was called safe by umpire Jim Reynolds on a close play. Price challenged the call, which was upheld.
The Reds meet the Rangers Monday afternoon at 3 35 with the action on Fox Sports 1360.