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.
Reds: Cueto said he chatted briefly with Angels slugger Albert Pujols during the game.
Speaking through a translator, the right-hander said Pujols told him he was throwing too many different pitches and that he wanted a fastball.
''I'm working,'' Cueto replied.
Pujols had spoken out strongly against Cueto before. Both players were involved in a nasty brawl between the Reds and Cardinals years ago in which Cueto kicked and spiked St. Louis pitcher Chris Carpenter.
Angels: Skaggs threw 32 of 50 pitches for strikes and is working on his curveball this spring.
''It's nice to go out there and throw strikes,'' said Skaggs, acquired in the three-way trade that sent Mark Trumbo to Arizona. ''I threw some good curveballs today and some not so good. It's a work in progress.''
Randy Marsh, Director of Major League Baseball Umpires, explained to reporters during the game that the call involving Conger at second base would have been overturned had the umpires been able to see the replay from the Angels' television broadcast.
Marsh said the umpires were unable to tell from the four replay cameras Sunday whether Reds shortstop Ramon Santiago tagged Conger. Marsh added that the fact that Angels fans could view the play was ''an umpire's nightmare.''
Price did not sound upset about the call after the game and said he was happy to see the umpires converge. He added that had one of the umpires seen something else on the play, the onus would have been on Scioscia to challenge the call.
''They went and did what they needed to do,'' Price said. ''This is pretty interesting stuff.''
The time of the appeal was 2 minutes, 50 seconds.
''They're getting less confusing as we go along,'' Scioscia said.
Angels: Left fielder Josh Hamilton (strained left calf) took batting practice on the field before the game.
Hamilton told reporters he was ''ahead of schedule'' and felt good. He said if he could play in a week, that would be good.
''We're not going to do anything stupid,'' he said. ''Give it a couple of days of feeling good.''
Tuesday will mark the second full week of Hamilton being off the field, which was the minimum prognosis.