All-Star closer Aroldis Chapman fanned two in his one inning of work, and the Reds got five hits off starter Ross Detwiler in a four-run second.
DeSclafani was acquired from Miami in the offseason trade that sent Mat Latos to the Marlins. The right-hander permitted four hits and wriggled out of a bases-loaded jam in the sixth after issuing two of his three walks.
''To his credit, he made his pitch,'' Reds manager Bryan Price said.
Brandon Phillips and Zack Cozart had run-scoring singles off Detwiler, obtained in an offseason trade with the Nationals. The left-hander was scheduled to face the Reds last Thursday but the game was rained out.
''We put the ball in play and when you do that, good things happen,'' Price said. ''We played good situational baseball.''
The four-run inning marred an otherwise solid outing for Detwiler. Two of Cincinnati's hits were bad-hop singles.
''I remember a couple pitches that were higher than I thought,'' Detwiler said. ''When you do that, you get the high chops.''
Rangers manager Jeff Bannister said: ''Detwiler had to get five outs in that one inning.''
''He got groundballs and most of the time that's good. Only a couple balls were hit solid,'' he added.
Adam Rosales made several nice plays to limit the damage.
''Rosales is a valuable guy to have,'' Bannister said. ''We can move him all over. He's done everything we've asked.''
Mitch Moreland had three hits for Texas, including a double.
Rangers: RHP Shawn Tolleson had an MRI on his stiff right forearm. ... OF Antoan Richardson is scheduled for surgery to repair a herniated disk in his lower back. ... OF Shin-Soo Choo, recovering from left triceps inflammation, played catch from 75 feet.
Reds: RHP Homer Bailey, out all spring after elbow surgery in September, will pitch in a minor league game Friday. ... RHP Johnny Cueto was due back in camp Wednesday. He had gone to the Dominican Republic due to an illness in the family.
Rangers: Detwiler is trying to win a spot in the rotation. ''He has done everything we'd like to see,'' Bannister said. ''There will be a decision shortly.''
Detwiler would like a couple of his pitches to be in better shape.
''I'd like to use my changeup more,'' he said. ''I have a little work to do on it. I would have liked to have gone five (innings). It is up to them (to make the decision). We have a lot of good pitchers around here.''
Reds: DeSclafani is a favorite to earn one of two open spots in the rotation. He was the second Cincinnati pitcher to go six innings this spring, following Jason Marquis on Monday. The 24-year-old threw 95 pitches. ''That was the highest pitch count I had,'' DeSclafani said. ''I was a little tired but I was still attacking hitters.''
Price knew DeSclafani was fatigued at the end.
''(Pitching coach Jeff Pico) went out to talk to him and said he was on fumes,'' Price said. ''In most of his starts, the last inning has been his most challenging. He's in a little different situation than a lot of our pitchers. He doesn't know if he's made the team. He brings a greater sense of need to perform. He's handled it really well.''
Texas sent 1B Mike McDade to the Baltimore Orioles for future considerations.
Rangers: RHP Nick Martinez will pitch Thursday night against Colorado RHP Chad Bettis.
Reds: RHP Michael Lorenzen makes his first spring start Thursday against Cleveland RHP Danny Salazar.