Moreland had two hits and drew a walk. He had not played since straining his left oblique March 18.
''It's significant that he's had good at-bats against everybody,'' Rangers manager Ron Washington said. ''It is big that he's handled left-handers. It looks like the new approach he has, not stepping in the bucket that he's staying in there pretty good.''
Alex Rios and Robinson Chirinos also contributed RBI singles in the Rangers' big inning.
Alberto Callaspo went 3 for 3 for the A's and is 12 for 28 (.429) in his past 10 games. John Jaso singled home a run, giving him eight RBIs in his past eight games.
Rangers right-hander Ryan Feierabend gave up four hits in four scoreless innings.
''I thought he was good,'' Washington said. ''He held them down to zeros for a pretty good while. He used all his pitches, threw the ball well.''
A's minor leaguer Sean Murphy limited the Rangers to one single over 4 1-3 scoreless innings in his debut against big league hitters.
''It was definitely nerve-wracking,'' Murphy said. ''That first inning I was so nervous. When you see a lineup like that, who wouldn't get a little nervous?''
''It was a blast. I can't even put it into words. I'm just super pumped right now. Getting big names out is definitely a key, so I'm definitely proud of that. That lineup is super tough,'' he said.
A's: Murphy, a 6-foot-6 righty from Philadelphia who was a 33rd-round pick in 2010, said he had never met manager Bob Melvin before Monday morning.
''I didn't even know I was starting until I saw the lineup in the major league clubhouse,'' Murphy said. ''It was my first time actually to be in the major league clubhouse. It felt good to get over there and experience it firsthand.''
Rangers: Feierabend had given up eight hits and two walks to the previous dozen batters he faced in his past two outings. He allowed three hits to the first four Oakland batters he faced, but got out of the inning unscathed thanks to an A's baserunning blunder.
A's: Second baseman Nick Punto left in the third inning with left hamstring tightness. Outfielder Craig Gentry (lower back strain) and right-handed reliever Ryan Cook (sore shoulder) will begin the season on the disabled list. They are active in minor league games, so they could be activated early as April 4. Melvin said he expects both could be ready by the fifth game of the season.
Texas ace Yu Darvish played catch for 10 minutes Monday, his first activity since being scratched from a minor league start Friday with a stiff neck. It still remains iffy whether he will be ready to start the March 31 opener. He will be reevaluated Tuesday.
PITCHERS ON BACK FIELDS
A's starter Dan Straily and relievers Sean Doolittle, Luke Gregerson and Jim Johnson pitched in a minor league game. So did Rangers left-hander Martin Perez, who threw 102 pitches in six innings in an intrasquad game. Perez allowed four runs and nine hits, facing mostly Triple-A hitters.
Straily yielded seven earned runs on 10 hits and walked two in 5 2-3 innings. Gregerson and Doolittle each tossed a scoreless inning, while Johnson surrendered two runs.
With Texas and Oakland meeting 19 times in the regular season, the managers preferred not to have their top pitchers face a division opponent late in spring training.