Danks, making his second start of the spring, struck out one and walked three as he continued his buildup to the regular season. He excited his surgically repaired shoulder feels strong.
"I feel like I can go after guys a little more aggressively," Danks said. "Got some movement on the fastball and the cutter's sharp. I'm like a kid in the clubhouse now and I'm excited to contribute."
Gordon Beckham hit a solo home run in support of Danks.
Saunders, signed last week to compete for a spot in the Texas starting rotation, gave up three runs and six hits in three innings, striking out four. Tommy Hanson, another starting rotation candidate, pitched the next four innings.
"We have some more time down here for him to work it out," White Sox manager Robin Ventura said of Boggs.
Texas: Saunders had a blister on the instep of his left foot but pitched through it.
"I had to get through three innings so just gutted it out," Saunders said. "I made a couple of mistakes they hurt me on but other than that, felt my arm was good. The ball was coming out well. I was throwing strikes."
Chicago: Danks had his cut fastball working and got some defensive help behind him.
"That's probably what I'm most pleased about," Danks said of his cutter. "My location wasn't where I wanted to be but it is spring training. Certainly something I'll work on."
Rangers right fielder Mitch Moreland dropped a fly ball off the bat of Alexei Ramirez that should have ended the first inning. In the top of the second, Moreland was doubled off first base on a fly out by teammate Engel Beltre, though it was on a hit-and-run call. In the fourth, Moreland was doubled off at first again on a lineout to shortstop.
White Sox center fielder Adam Eaton displayed a strong throwing arm in throwing out Moreland and also doubled in the first inning and scored. Danks said they appreciate Eaton's "dirtbag" playing style.
"You can't change anything," Eaton said. "You have to continue to work on what you work on. At the end of the day you put it all out there and that's what you're going to get."
The Rangers' Robinson Chirinos reached base three times and drove in a run, and is now 7 for 15 in spring training.
"Right now he's the hottest hitter in the Cactus League," Rangers manager Ron Washington said of Chirinos. "That says it all. Seven for his last seven getting on base. He's seeing the ball well."
White Sox third baseman Matt Davidson hit a solo home run to tie the game at 6 in the bottom of the eighth inning in his only at-bat of the game.
Rangers: Infielder Kensuke Tanaka cracked three teeth playing second base and taking a pickoff throw in Monday's game. Tanaka was scheduled to see a dentist Tuesday in nearby Mesa. ... Infielder Brent Lillibridge returned from a thumb injury and was a late-inning replacement Tuesday, collecting two hits. ... Outfielder Alex Rios is day to day with a strained ribcage. ... Pitcher Derek Holland is throwing 60 feet as he recovers from knee surgery. ... Infielder Jurickson Profar has yet to take the field but was used at designated hitter Tuesday. Profar is taking infield and throwing from 120 feet in workouts as he deals with shoulder soreness. He went 1 for 3.
White Sox: Pitcher Matt Lindstrom is day to day with an oblique injury and is back to playing catch.