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ST. LOUIS -- Ryan Dempster's winless streak is now at 15 starts. But the Chicago Cubs took a step forward with their luckless pitcher.

"It's alright. Baby steps," Dempster said after the Cubs sent the St. Louis Cardinals to their fourth straight loss at home with a 6-4 victory on Monday night. "We got a win when I started a game."

Alfonso Soriano singled in the go-ahead run in the eighth inning and Bryan LaHair had three hits, including a two-run homer -- his ninth overall and fourth against the Cardinals -- to break a 1-for-14 slump. Chicago's runs in the eighth and ninth innings came too late for Dempster, whose last victory was Aug. 16 against the Nationals.

Shawn Camp (2-1) allowed one hit in two innings of work and Rafael Dolis worked the ninth for his fourth save in six chances for the Cubs, who won for only the fourth time in their last 13 games in St. Louis despite stranding a season-worst 14 runners.

Jake Westbrook became the latest Cardinals starter who couldn't pitch deep into the game, allowing four runs on 11 hits in five innings. Of the other four pitchers during this run through the St. Louis rotation, only rookie Lance Lynn lasted six innings.

"I didn't feel any added pressure, I put that on me every night no matter what the situation is," Westbrook said. "I just didn't get the job done."

The Cardinals got swept by Atlanta over the weekend and hadn't lost four straight at home since a five-game skid Aug. 14-20, 2010.

"Over the course of the season you're going to have little ruts where you're not getting the breaks and when you're not playing well that compounds the problem," Lance Berkman said. "This team's got a lot of character. We knew it wasn't going to be smooth sailing the whole year."

Dempster gave up four hits over the first five innings before surrendering four runs on five hits in the sixth that tied it 4-4. Three of Dempster's first five innings were perfect and he retired 10 of 11 batters from the second to the fifth inning -- totaling just 27 pitches.

Soriano's go-ahead RBI single off Mitchell Boggs (0-1) salvaged the Cubs' eighth after the Cardinals turned an unusual 3-5-4 double play earlier in the inning. Berkman, the first baseman, fielded Starlin Castro's popped-up bunt and threw to third to force David DeJesus, then David Freese's relay to first was there in plenty of time to get Castro.

The Cubs still had Tony Campana on second, and after LaHair was intentionally walked, Soriano's first hit in 10 career at-bats against Boggs -- seven of them strikeouts -- gave them the lead.

"It wasn't a scalded dog, it just got out of the infield," Cardinals manager Mike Matheny said. "It's just where we are right now, we're just going to have to fight."

Freese's wild throw to first in a bid for a double play on another bunt allowed an insurance run to score in the ninth against Boggs. The Cardinals committed a season-high three errors, two in the ninth.

Dempster entered with a majors-best 1.02 ERA, the lowest for a Cubs pitcher winless through the first five starts since the NL began tracking earned runs in 1912. He is 0-1 mainly because the Cubs have totaled just eight runs combined in his starts. The Cardinals got to Dempster after the Cubs' four-run sixth, and the right-hander exited with a 1.74 ERA.

LaHair's two-run homer was the highlight of the Cubs' four-run fifth, and he added a pair of singles and his first career steal in the seventh.

"I just wanted to slow things down," LaHair said. "I came off a rough series and I just wanted to get back on track and hit the ball hard and help the team."

Yadier Molina's two-run double and Skip Schumaker's tying RBI single were the key hits in the Cardinals' four-run sixth. Schumaker is a career .431 hitter against Dempster, the best ever against the right-hander with a minimum of 30 at-bats, according to STATS LLC.

One of the early hits in the rally was Matt Holliday's liner off the left-field wall that gave Soriano a perfect rebound to hold him to a single.

Game notes:

The Cardinals' Carlos Beltran, who entered with six homers in six games and a NL-leading 13, did not start due to knee soreness and Matheny wasn't sure whether Beltran would be in the lineup for the finale of the two-game series Tuesday afternoon. Beltran is 6 for 12 against Dempster with a homer and three RBIs. ... The three-hit game was LaHair's third of the season, matching his career best. He has reached base safely in 31 consecutive games and is 8 for 19 with eight RBIs against the Cardinals. Berkman has reached safely in a major-league high 33 games. ... The Cubs have scored three or fewer runs when Dempster was in the game 13 times during his winless drought. ... Rafael Furcal was 0 for 5, ending a 12-game hitting streak in which he batted .510 (25 for 49) with two homers.