PITTSBURGH -- Winning a career-best five straight starts might not be enough for Kevin Correia to keep his spot in the Pittsburgh Pirates' starting rotation.

Correia gave up two runs and four hits in six innings, helping Pittsburgh beat the Chicago Cubs 3-2 and avoid getting swept at home from the first time since Sept. 9-11 against the Marlins.

"Kevin is a grinder," Pirates second baseman Neil Walker said. "The way he pitched today is the way he always pitches. He doesn't overpower anyone, but he just keeps battling and battling and he gave us a chance to beat a very good pitcher."

Garrett Jones drove in the go-ahead run with a two-out double in the sixth inning. Walker and Michael McKenry homered for Pittsburgh.

Ryan Dempster (5-5) lost in what might his last start for Chicago, allowing three runs and five hits with in six innings with six strikeouts and no walks. Dempster said he is mulling a decision to accept a trade to Atlanta and is also "keeping all my options open."

Chicago is off Thursday, and Dempster said he'll spend part of the day thinking about his situation. He has the right to veto any trade as a 10-and-5 player -- at least 10 years of major-league service time, including at least five with his current team.

The deadline for trades without waivers is Tuesday.

"I'm definitely going to think about Atlanta," Dempster said. "I know (Braves GM) Frank Wren from my days in Florida, when he was the assistant GM there. I have a lot of respect for (manager) Fredi Gonzalez. I don't know what I'm going to do. I have a few days to think about it before the trading deadline."

His ERA, which had been a major league-leading 2.11, rose to 2.25.

Despite his winning streak, Correia (8-6) has a 4.82 ERA in his last five starts and is a candidate to be moved to the bullpen following the acquisition of left-hander Wandy Rodriguez from Houston on Tuesday. Pirates manager Clint Hurdle said before the game that he might also consider going to a six-man rotation, at least temporarily.

"We acquired a very good pitcher who is going to help us," Correia said. "Somebody is going to have to come out of the rotation. I thought about it a lot last night, but it wasn't on my mind when I took the mound. I just tried to do the best I could to help the team win and the decisions about the rotation are out of my hands."

Relievers Jared Hughes, Jason Grilli and Joel Hanrahan followed Correia with one scoreless inning each. Hanrahan recorded his 29th save in 32 chances.

"That back end of the bullpen is as good as it gets," Chicago manager Dale Sveum said.

Pittsburgh entered the day leading the NL wild-card standings, and was 2½ games behind Cincinnati in the NL Central.

The Pirates pulled ahead 3-2 in the sixth inning when Jones lined a double that scored Alex Presley, who singled with one out and took third on Andrew McCutchen's single.

"That was a good piece of hitting by Jones, because I threw a pitch that was really down and he went down and got it," Dempster said.

Dempster threw a water cooler in the Cubs' dugout after being lifted for a pinch hitter in the top of the seventh. He said his brief outburst was not partially a byproduct of the trade talk but came out of frustration over leaving the game.

"I have a lot of respect for (Sveum) but I don't always have to agree with every move he makes," Dempster said. "I'm allowed to be upset, but I was over it as soon as I got to the clubhouse."

Both teams hit solo home runs in the first. Anthony Rizzo connected for his fifth with two outs for Chicago and Walker countered with his ninth in the bottom half.

The Cubs went back ahead in the fourth as Rizzo singled in David DeJesus, who had doubled, with two outs. The umpires upheld their ruling on DeJesus' double after a video review showed a fan had touched the ball before it went over the center-field fence.

Pittsburgh tied the score when McKenry hit a two-out solo homer off the left-field foul pole in the sixth. Dempster retired 13 batters in a row between the home runs by Walker and McKenry.

"We're a very resilient team," McKenry said. "Dempster was pitching great but we found a way to come back and beat him. It was a really good win for us."

Game notes
Chicago LF Alfonso Soriano got the day off after going 4-for-8 with two home runs and four RBIs in the first two games of the series. ... Rodriguez is expected to join the Pirates on Thursday in Houston when they open a four-game series against the Astros. Rodriguez pitched Monday night against Cincinnati, so the earliest he would likely be able to pitch is Saturday. ... RHP A.J. Burnett (11-3, 3.59) is scheduled to start for the Pirates on Thursday night against LHP Dallas Keuchel (1-2, 4.03). ... Chicago opens a three-game series Friday against St. Louis. LHP Travis Wood (4-5, 4.33) is the probable starter for the Cubs and will face RHP Lance Lynn (12-4, 3.10).