Jackson allowed one run and three hits in six innings as the Cubs rested most of their regulars in a 5-2 win over the San Diego Padres.
"I'm getting closer and closer to game mode," Jackson said. "The goal is to keep heading in a positive direction as we get closer to the regular season."
Jackson left his No. 36 jersey behind at the Cubs' clubhouse in Mesa and wore No. 82 instead. He struck out three and walked one.
San Diego pursued him but wouldn't guarantee a fourth year, and Jackson signed a $52 million, four-year deal with the Cubs, his ninth organization.
"The one thing I knew was that I could end up anywhere," Jackson said. "In free agency, you just never know how things are going to go, and I was ready for anything and ready to go anywhere. The transition hasn't been bad. I've worked to get acclimated with the system and a new group of guys. It's a pretty welcoming clubhouse, and that makes it easy to get used to a new team."
Padres starter Clayton Richard allowed Javier Baez's RBI groundout in the fourth and Dave Sappelt's three-run homer in the fifth. Richard gave up five runs and seven hits in 6 2/3 innings, struck out four and walked none. He recorded 10 outs on grounders.
Richard also had an RBI single in the fifth.
"The adjustment really seemed to help," Padres manager Bud Black said. "He let his arm get up a little higher, and that resulted in more sink and more consistent pitches throughout the day. The ball had a lot of action and was down in the zone. We were pleased with it. I know Clayton was too."
The Cubs used reserves after three days of split-squad games and plan to start their regulars on Tuesday.
Padres LF Carlos Quentin played his second minor league game in as many days, and went 3 for 6 with a home run and two singles in six plate appearances. Quentin has been out most of spring training because of a knee injury. ... INF Logan Forsythe (plantar fasciitis) is close to a return to game action. ... RHP Casey Kelly will seek a second opinion on his ailing right elbow this week and will make a decision on whether to have elbow ligament- replacement surgery. ... The Padres optioned RHP Mile Mikolas to Triple-A. ... The Cubs officially reassigned INFs Junior Lake, Christian Villanueva, Josh Vitters and Javier Baez, OF Jorge Soler, C Rafael Lopez, RHP Barret Loux to their minor league camp.