Darvish, who will start the Rangers' March 31 opener against Philadelphia, gave up two runs and four hits in 4 2/3 innings. He struck out three and walked three.
"It wasn't very good, but I was able to grind out," Darvish said through an interpreter. "I was working on my fastball and also my two-seam and because I threw too many of my cut fastball, I wasn't able to get a lot of strikes."
Adrian Nieto's two-run single with two out in the fourth was the only damage off Darvish.
"You can see that's how good he is," Arencibia said. "If he's out there working on some things and still being able to dominate games. I think he's right where he needs to be and hope will continually to get better."
Arencibia's sixth-inning grand slam gave the Rangers an 8-3 cushion, but the White Sox scored five runs in the seventh, highlighted by Paul Konerko's three-run double.
White Sox: Left-hander John Danks, who had not allowed a run in eight innings in his first two starts, gave up three runs and seven hits in five innings.
"I thought he threw great," manager Robin Ventura said. "We didn't really help him out (defensively) in the first inning. He battled. I think that's the one thing he's going to do. He threw deep into the game pitch-wise and that's all we're asking him to do right now. He just feels confident. I think that's the biggest thing compared to where he was the last year and a half."
Rangers: Darvish threw 84 pitches, 48 for strikes, and then went to the bullpen to get more work in.
"I just wanted to make sure my delivery was OK," Darvish said. "Since I threw many cutters during the game, I felt a little bit off with my delivery, so that's why I wanted to make sure it was OK."
ARENCIBIA IS GRAND
Arencibia connected against Zach Putnam for his first spring homer.
"My first few at-bats I was trying to take some pitches and see the ball and try to hit it later in counts," Arencibia said. "In that at-bat, bases loaded, I was going to be a little bit more aggressive.
"It was a good swing. I knew I hit it hard. I didn't know if it was going to be enough to get over the fence. It was a line drive, so those are kind of tough sometimes, but it was enough."
White Sox: With Gordon Beckham out at least seven days with a strained left oblique, Marcus Semien and Leury Garcia will get the majority of the time at second base. Closer candidate Matt Lindstrom, who has been out with a strained left oblique, could make his Cactus League debut this week.
Rangers: Jurickson Profar made relay throws from second base to first base for the first time in Sunday drills. Profar, who has been hampered by right shoulder tendinitis, will likely play in the field for the first time Monday against the Royals. Third baseman Adrian Beltre missed his third straight game with a strained left quadriceps.
CLOSING CANDIDATES PERFECT
Neftali Feliz and Joakim Soria, the Rangers' top two closing candidates, retired all six batters they faced. Feliz struck out two in the eighth, while Soria struck out one in the ninth. Soria has not allowed a run and only two hits in five innings in five appearances.