Cueto also had five strikeouts, twice fanning Prince Fielder, in a bid to start on opening day.
''Cueto looked great. His velocity was up, not that it's paramount but it seemed like he did,'' Reds' manager Bryan Price said. ''He had a real good cut fastball, sinker and four-seamer, that's three different pitches off the same pitch. ... You add a cutter to that and that's how Greg Maddux made a beautiful living.''
Manny Parra earned the save, striking out two in a hitless ninth.
Michael Choice doubled off Cueto in the second and singled home the only run off Cueto in the fourth.
''Cueto just got a slider up to Choice that he hit for the single that scored their run,'' Price said.
Hamilton is taking over the center field and leadoff spot that Shin-Soo Choo held last season. Hamilton reached base twice and stole his seventh base of the spring in as many tries. Hamilton set a professional record with 155 stolen bases in the minor leagues in 2012.
Choo, who signed with Texas as a free agent, was 0 for 4 against his former teammates as the designated hitter.
Rangers: Scheppers started for the Rangers. Scheppers, who worked out of the Texas bullpen last season is in a competition with Robbie Ross, Joe Saunders, Tommy Hanson, Nick Tepesch and Colby Lewis for two open spots in the starting rotation.
Scheppers pitched three innings, allowing two runs on three hits and two walks. He struck out five.
Two of the three hits came in the second inning, when Cincinnati scored the two runs.
''I made a mistake to (Zack) Cozart and he took advantage,'' Scheppers said. ''I had to bear down after that.''
The transition from bullpen to starter has its challenges.
''As a reliever, I could come in and just use my power stuff,'' Scheppers said. ''As a starter, I have to pace myself. I have to pitch instead of throw.''
Scheppers and Ross went head-to-head in the competition for a starter's job and Texas manager Ron Washington had a good look.
''Tanner worked around some issues early and made pitches when he had to,'' Washington said. ''
Reds: Cueto was scheduled to pitch five innings. The Reds still have not named the opening day starter, but Cueto, who is coming off an injury-riddled season, is considered the favorite.
''I am waiting on Bryan Price to let me know if they want me to start opening day,'' said Cueto through interpreter Tomas Vera.
Cueto was the first Reds' pitcher to finish five innings.
''I was just working on keeping the ball down and landing straight instead of falling off to the right,'' Cueto said. ''I was happy that I could do that.''
Robbie Ross was sharp for the Rangers in his four innings. Ross allowed five hits, but didn't walk a batter to hold the Reds scoreless.
''Ross worked on both sides of the plate and kept the ball down,'' Washington said.
Ross has had a problem getting left-hander hitters out, but seems to have that corrected based on this game.
''He used both sides of the plate and was throwing the ball well,'' Washington said.
Rangers: Adrian Beltre left Thursday's game with a mildly sprained left quadriceps. He is day-to-day. ... Second baseman Jurickson Profer had four wisdom teeth removed and has tendinitis in his right shoulder. ... Infielder Kensuke Tanaka broke three teeth in a game against Cincinnati on Monday. He is playing but still getting dental work. ... Left-hander Matt Harrison was also considered among the pitchers competing for the rotation but is trailing the others with back pain. He threw live batting practice this afternoon in Surprise.
Reds: Matt Latos threw live batting practice in the afternoon. Latos had bone chips removed in October and the meniscus in his left knee repaired on Feb. 14. Price is optimistic that Latos, barring a setback, could start on April 6. The Reds will not need a fifth starter until then. Latos is tentatively scheduled to make his spring debut on Wednesday. ... Jonathan Broxton's elbow surgery was more serious. He will make his initial spring appearance on Wednesday. ... Left-handed reliever Sean Marshall threw his first bullpen on Friday. He is not expected to be ready by the start of the season. ... Jack Hannahan had shoulder surgery in October. He was the designated hitter on Friday in his first live action of the spring.
Choo accepted the Most Valuable Player Award from the Cincinnati chapter of the Baseball Writers Association of America before the game. Choo, who signed with Texas in the offseason, was presented the award by John Fay of the Cincinnati Enquirer. Choo tipped his cap to the Reds players, who applauded Choo for his efforts as their teammate last season.
The game was played in 2:13. It is the shortest time of game for the spring at Goodyear Ballpark.
The Reds optioned catcher Tucker Barnhart and RHP Curtis Partch to Triple A Louisville. They have 42 players remaining in camp.