Jackson threw six scoreless innings, allowing five hits with three walks and two strikeouts in Arizona's 10-1 victory over the Chicago White Sox.
"His delivery was significantly better," Diamondbacks manager A.J. Hinch said. "He wasn't jumpy or out of control like he had been his last couple of outings. He was very much in control of the game."
Jackson also had some success with the bat with a single off Chicago starter Freddy Garcia in the third inning and a sacrifice bunt in the fourth. After his single, he advanced to second on a single to right field and then to third on a forceout before scoring on Justin Upton's three-run home run.
"I got a single and (it was) kind of a circus on the bases," Jackson said with a laugh. "A good thing I still scored. Get a hit, try to help myself out a little bit."
He said he shook off few signs from catcher Chris Snyder.
"I was just finding a rhythm, going out there and keeping a nice tempo, making adjustments from pitch to pitch instead of waiting until the inning snowballed to make an adjustment," said Jackson, Arizona's No. 2 starter behind Dan Haren.
Garcia gave up seven runs and 11 hits in five innings for the White Sox. Garcia, slated to be Chicago's fifth starter, struck out three and walked one.
White Sox manager Ozzie Guillen said he isn't concerned with the veteran right-hander.
"When the lights are on and things get going, Freddy is a different pitcher," Guillen said. "Right now, Freddy is going through to get his stuff and is climbing a bit to get there and get ready. That's why I'm not worried about it yet."
Upton hit his fourth home run of the spring off Garcia to right field in the third inning. Upton returned to the lineup after sitting out Thursday because of an ankle sprain.
Tony Abreu, a candidate for Arizona's bench, went 3 for 5 with a double and five RBI.
"He's really been impressive this spring," Hinch said. "I'm happy with how he's played since Day One. He hasn't missed a beat."
In a separate game, right-hander Kris Benson threw against Rockies minor leaguers. He allowed two runs and four hits -- including two doubles -- struck out three and walked three in five innings. He signed a minor-league deal with the Diamondbacks and is a candidate for the No. 5 spot in the starting rotation, which Arizona won't need until April 17. He spent eight years in the majors with the Pittsburgh Pirates, New York Mets, Baltimore Orioles and Texas Rangers.
The Diamondbacks' Mark Reynolds and Chris Young each had three hits. ... Sox 2B Gordon Beckham was scratched from the lineup because of tightness in his left side. Guillen said Beckham is day-to-day and the tightness is not serious. Jayson Nix replaced Beckham at second base.