Jackson allowed only a ground single to Aaron Hill and did not walk a batter. The right-hander struck out two and threw 34 of 47 pitches for strikes.
Jackson, who lost a major league-high 18 games last season, is scheduled to start Wednesday in Pittsburgh.
Ryan Sweeney and Nate Schierholtz each had an RBI single and made a diving catch in the outfield to back Jackson.
''I'm feeling pretty good,'' Jackson said. ''Just coming out throwing strikes and letting the defense play behind you.''
Diamondbacks starter Trevor Cahill gave up three runs and eight hits in six innings. It was Cahill's first start since he took the loss against the Dodgers in Arizona's second regular-season game in Australia on Sunday.
''I thought he was better tonight,'' Diamondbacks manager Kirk Gibson said. ''He had better rhythm. He controlled the count better.''
Cubs right-hander Armando Rivero struck out Tuffy Gosewisch with the bases loaded to end the eighth.
Jose Veras gave up a hit and hit a batter with a pitch in the ninth before securing the save.
Cubs: Jackson lowered his spring ERA to 4.00. It was 4.98 during his forgettable 2013 season.
''I'm excited,'' Jackson said. ''Last year was a crazy year, not a year I wanted to have. I'm eager to go out and be able to play the way I know I can play. I haven't lost any confidence.''
Diamondbacks: Cahill walked three and struck out five, throwing 55 of 92 pitches for strikes. Gibson said the team is trying to get Cahill to speed things up.
''His pace was much better,'' Gibson said. ''We're trying to get him on the mound and go.''
Cubs manager Rick Renteria announced Carlos Villanueva will be the team's fifth starter and Chris Rusin will be sent to Triple-A.
The 30-year-old Villanueva had a 5.60 ERA in six spring training appearances. The 27-year-old Rusin gave up four home runs in his last spring start Wednesday.
The Villanueva decision left the Cubs with only the bullpen to sort out before setting their 25-man roster.
Left-hander Zac Rosscup, contending for a spot, allowed one hit and one walk with two strikeouts in two scoreless innings.
BAD ELBOWS HERE
''It's not something you want to wish on anybody,'' Corbin said.
The All-Star left-hander was greeted warmly by teammates as he rejoined the club after Tommy John surgery Tuesday. The team was coming to grips with the news that Hernandez, the Diamondbacks' setup man, also has a torn ulnar collateral ligament and is likely out for the season.
''It's a long process, but I have people around here to talk to,'' Hernandez said.
Left-hander Matt Reynolds and right-hander Daniel Hudson, who has had the surgery twice, also are recovering from the same injury.
Cubs: Shortstop Starlin Castro, who has been playing in minor league games this week as he recovers from a strained right hamstring, could play in the final exhibition Saturday against Arizona.
Diamondbacks: Outfielder Cody Ross (hip) has been playing in camp games and remains on track to return next month. ''Everything is still pointing in the right direction,'' Gibson said.
Arizona players were learning the details of the new drug agreement as they came to the park Friday.
It includes increased testing, an 80-game suspension for the first offense, and a 162-game ban for a second offense. Players who test positive also will be banned from postseason play.
''As a union, we're excited,'' said right-hander Brad Ziegler, the team's union representative. ''The goal is a clean game. And a lot of things we got done were player-driven. I think that shows how much the players want the game clean.''
REDSKINS & DIAMONDBACKS
Quarterback Robert Griffin III was one of several Washington Redskins players to take swings in the Diamondbacks' indoor batting cage Friday. Griffin then posed for pictures with Arizona players.