Jackson allowed three hits, walked one and struck out six.
"It was one of those (outings) where you come out and pitch when you don't necessarily have your best stuff," he said. "I had to throw a lot of pitches for strikes and fortunate enough to get out of some jams early.
"It's the time now when you can really work on pitch selection, stretch the innings and now worry about the results."
Jackson struck out Carlos Pena with the bases loaded to end the first inning.
Joe Blanton pitched 5 1/3 innings for Los Angeles and was charged with three runs and four hits. The veteran right-hander has pitched well since moving from the first-base side of the pitching rubber to the third-base side before his last spring start.
Angels: Blanton is pitching for the scouts as much as he is for a spot on the team. The team hasn't said if he is up for a rotation spot after going 2-14 with a 6.04 ERA last season.
After allowing nine earned runs in his first 5 2/3 innings this spring, he has allowed three earned runs over his last 10 1/3 innings for an ERA of 6.75 in four games.
"That's the way of the world," Blanton said recently. "That's the business we're in. It turns into, `What have you done for me now?' "
Cubs: Jackson was making his first spring start since March 7. He had a minor league outing in between his Cactus League starts, and feels he is on schedule.
"I'm pretty close," he said. "The main thing is being comfortable, being able to go out have a steady rhythm every time. I've been working on having the hitters put the ball in play and I've been able to do that."
Cubs: Mike Olt was scratched from Monday's game in Phoenix against the A's with a fatigued right throwing shoulder. He has played in nine games as either a designated hitter or a first baseman.
He is expected to compete for the third-base job and feels there is still time to show he can be the everyday starter.
"As long as I'm healthy, I know what I'm capable of doing," said Olt, who is hitting .241 with three home runs. "Everyone in here becomes a point where you got to stay healthy. Everyone can stay in the big leagues. It's a matter of getting my body healthy and preparing for 162 games."
Cubs shortstop Starlin Castro said he thinks he will be ready for the season opener a day after running sprints at about 80 percent and taking some ground balls. He is expected to run the bases on Tuesday.
He has been hampered by a hamstring injury.
"I'm not too worried about Starlin, to be honest with you," Cubs manager Rick Renteria said. "His demeanor is pretty positive, pretty upbeat, and I think he's trying to get himself ready for the season."