Davis -- just the second left-hander to start against the Cubs this season -- struck out seven, walked three and hit a batter as the Diamondbacks won a series for only the second time this season.
Tracy had three hits, including a two-run double and a solo home run. Upton brought three more home with a double in Arizona's five-run seventh inning. The Cubs walked 10, eight in the last two innings, including three with the bases loaded, to finish their road trip 2-4.
"We're not going to be able to just go out there and play without intensity and go through the motions and think we can win baseball games, I can tell you that," Cubs manager Lou Piniella said, "and the quicker that sinks in, I think, the better."
Tony Pena and Juan Guitierrez finished off Arizona's third shutout of the season, the second involving Davis, whose record is a deceptive 2-3 but with a 2.91 ERA. Two of Davis' past three starts have been shutout victories.
"Fifty pitches after two and he ends up going seven innings," manager Bob Melvin said. "... For a guy that tends to throw a lot of pitches and get himself in some jams, this stretch has been awfully good."
The Diamondbacks jumped on Ryan Dempster for three runs in the first. Felipe Lopez drew a leadoff walk and Augie Ojeda singled to put runners at first and third. Both scored on Tracy's ground rule double that bounced over the fence in right. Tracy advanced to third on Mark Reynolds' single, then scored when Eric Byrnes bounced into a fielder's choice.
Arizona made it 4-0 when Tracy lined the first pitch of the third inning into the right-field seats for his second home run of the year.
Dempster (1-1) threw six innings plus one batter, allowing five runs and six hits. He struck out four and walked three. But the Cubs' offense couldn't carry over the momentum from its 11-3 victory the previous night.
"I expected us to go out and hit him [Davis] a little better than we did, to be honest with you," Piniella said. "Give him credit, he changed speeds and located really, really well."
"I know they're an aggressive team and they swing a lot," Davis said, "so I was trying to get them to hit my pitch."
Six walks, one intentional, accounted for the first two runs in Arizona's big seventh. Dempster walked the leadoff batter, pinch hitter Ryan Roberts, then was relieved by Carlos Marmol. Marmol walked four of the five batters he faced, one intentionally to load the bases. His walks to Reynolds and Byrnes each brought home a run to make it 6-0.
Upton's bases-clearing, two-out double to the right-center gap off Jeff Samardzija made it 9-0. The 21-year-old outfielder got off to an awful start, but has hit safely in 11 of his last 13 games.
"It's getting there," he said. "I'm really getting some work in trying to lock into something that's comfortable for me, and it's coming along."
Kevin Gregg's bases-loaded walk in the eighth scored the 10th run.
Dempster, in his 200th career start, lost in April for the first time in 11 starts since returning to the rotation last season. ... The Cubs finished their road trip 2-4. ... Dempster dropped to 1-5 against the Diamondbacks. ... The 10 runs were the most scored by Arizona and most allowed by Chicago this season. ... After playing 18 of their first 21 games at home, the Diamondbacks open a nine-game road trip Thursday in Milwaukee.