Moreland went 2-for-3 and is now the only Rangers player with three home runs this spring. He also leads the team in RBIs, with 10, and is hitting .361. Last spring he hit .283 with three home runs and nine RBIs while recovering from offseason wrist surgery.
"I pretty much approach every spring the same," Moreland said. "This offseason I was able to get more done as opposed to the last offseason, when I was just trying to get back healthy. I feel pretty good, and it's coming along well. I'm trying to keep grinding it out. So far it has been a lot of fun."
Villanueva, who will open the season in the rotation because of injuries to Matt Garza and Scott Baker, gave up four hits and three walks over four innings while striking out two.
Lefty Robbie Ross, a candidate for the fifth spot in the Rangers' rotation, threw three scoreless innings, giving up four hits and walking three.
The Cubs loaded the bases in the third, but Ross got Dioner Navarro to fly out and end the inning.
Gallo's homer came off Esmailin Caridad in the sixth.
Nate Schierholtz greeted Collin Balester with a home run leading off the Chicago sixth to make it 6-1.
Chicago's Timothy Saunders closed the scoring with a two-run homer in the eighth, and the Cubs threatened in the ninth, loading the bases, but Chad Bell came in and struck out the final batter, Brad Nelson.
The Cubs and Rangers, who will square off in Interleague games from April 16-18 at Wrigley Field, split the weekend series at Cashman Field.
Up next for Rangers: Yu Darvish pitches for the Rangers at 8 p.m. CT Monday against the Royals in Surprise. Darvish has pitched 8 2/3 innings this spring, allowing one run on five hits, walking two and striking out 10. Derek Lowe is also scheduled to pitch in his second outing with the Rangers since being signed to a Minor League contract. He threw two scoreless innings against the Giants on Friday.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.