PHOENIX -- The Cubs' sporadic success in 2010 can be likened to Ryan Dempster swiveling his mitt before each pitch out of the wind-up, cleverly hiding baseball from batter.

Now you see it. Now you don't.

But after three consecutive wins here in Phoenix -- guaranteeing its first series victory in six tries and just its second sweep of the 85-game-old season -- Chicago's on-again, off-again act is, well, on again.

Behind five solid innings from Dempster, four near-perfect frames from the bullpen and a third multi-run blast in 24 hours from Aramis Ramirez, the Cubs dropped the D-backs, 8-3, on Wednesday night.

"We haven't played like this in a while," said Dempster, who snapped a five-game losing streak against Arizona that stretched back to April 2001, despite being held to 98 pitches by his cautious manager. "We swept 'em, and it's huge for us. We need as many wins as possible. Our second half started and we've got to play better in the second half, and doing things like this really helps."

Of course, when the Cubs are going well, it's not necessarily about Dempster (7-7) or his fellow starting pitchers. Rather, their success hinges on an offense that's often been hampered by middling middle-of-the-order sluggers: in 38 wins this season, the Cubs are batting .290-plus and averaging 6.2 runs per game. In 47 losses, they are hitting .223 and plating just 2.3.

Perhaps most significantly this week at Chase Field, the Cubs were 10-for-26 with runners in scoring position.

"We have been waiting for our bats to come alive and, in this series here, we scored what, nine, eight, and six," manager Lou Piniella said. "Ramirez, what a difference. His three-run homer put [Wednesday's] game away there in the ninth.

"I like a lot of things I saw in this series. Let's continue it, that's all."

On cue, Chicago broke through against Arizona starter Edwin Jackson (6-7) in the fourth with two runs on a quartet of consecutive hits from Derrek Lee (single), All-Star Marlon Byrd (RBI double), Ramirez (single) and Alfonso Soriano (RBI single). Three batters later, Ramirez scored the Cubs' third run on Dempster's bloop of a bunt toward the mound.

"The first baseman and second baseman were playing way back," Dempster said, "so I thought if I could push a bunt that way, I didn't think they would turn two and I thought that it would get Rami home from third. I was able to just get it by the pitcher there, in the air more than I wanted to. To get a run there is big."

The D-backs loaded the bases against Dempster with one down in the fourth, and Jackson helped his own cause by popping an RBI single. The ensuing batter, leadoff man Chris Young, took advantage of his 3-0 count green light and pulled a Dempster heater down the third-base line to plate two and tie the score at 3.

The Cubs grabbed the lead for good in the fifth, however, first advancing a man to third base on Ryan Theriot's 100th career stolen base and later loading the bases with two outs. It paid off: Starlin Castro's single through the left side of the infield, a busy region between shortstop Stephen Drew and third baseman Mark Reynolds, drove in two runs for a 5-3 advantage.

"Seven of their 10 hits were between the five-six hole, five of them off Edwin," lamented D-backs interim manager Kirk Gibson, who has lost five straight since his victorious debut at the helm. "In the fifth inning, I think there were three of them. That's a killer."

In the midst of Chicago's fifth-inning rally, though, Soriano suffered a left elbow contusion when he was struck by a 94-mph Jackson fastball. Tyler Colvin replaced him in left field in the bottom of the inning, but Piniella said he would likely slot Soriano in the starting lineup on Thursday against the Dodgers' Clayton Kershaw, the first game of Chicago's final series before the All-Star break, and rest him on Friday if need be.