MINNEAPOLIS -- It's been an underwhelming start to Jeff Samardzija's career with the Chicago White Sox. But if the last three outings are any indication, the right-hander may finally be getting back on track.

Samardzija (5-4) allowed just two runs over seven strong innings as the White Sox won 6-2 over the Minnesota Twins at Target Field on Tuesday.

For Samardzija, traded to Chicago over the winter from the Oakland Athletics, it was his third consecutive outing of at least seven innings and was his third straight quality start.

"I was just in the zone, stayed away from their power guys," Samardzija said. I just didn't want to pitch into any damage."

Unlike Monday's series opener, when the Twins were able to put together a pair of big innings, Samardjiza deftly navigated Minnesota's lineup. He gave up a solo homer in the first inning then allowed one other run when three straight men to reached with two outs in the fourth.

A fine defensive play by shortstop Alexei Ramirez on a cutoff throw from left field limited the inning to one, and the White Sox offense picked up their pitcher after that.

"I thought I was better out of the wind up," Samardzija said. "Early on, if I'm not grooving out of the wind up I put myself in tougher positions out of the stretch. I thought I got some quick outs. If you can get that first out out of the way with nobody on, you can settle down after that."

Chicago first baseman Jose Abreu had a career-high four hits and scored two runs. Center fielder Adam Eaton had three hits and an RBI, and catcher Geovany Soto added a pair of RBI singles.

Twins right-hander Mike Pelfrey (5-4) gave up three runs on 10 hits and three walks in 6 2/3 innings. He struck out four.

"Coming in, I knew it was going to tough out there with how good (Samardzija) is," Pelfrey said. "He out-pitched me. That's the story right there, he was good."

Soto's second RBI single tied the score at 2-2 in the sixth inning before the White Sox took control. An RBI single by left fielder Melky Cabrera gave Chicago the lead for good in the seventh.

Eaton's double in the eighth increased the margin to 4-2. In the ninth, a single by first baseman Adam LaRoche and a double by third baseman Gordon Beckham, a late-inning defensive substitution, tacked on runs.

"Good at-bats, the guys just kept grinding away," White Sox manager Robin Ventura said. "Anytime you add on and keep getting those to fall or squeak through, you wear out the other side."

The Twins took the first-inning lead on a solo home run by left fielder Eddie Rosario, who golfed a knee-high fastball over the wall in right field for his fourth homer of the season.

"We saw that (with Samardzija) the last time we were in Chicago He gave up some runs early and found a way to get through eight innings," Twins manager Paul Molitor said. "You get a lead off of him and you're probably going to have to find a way to hold on because he gets stronger as the game goes on."

Chicago evened the score in the fourth. A one-out double by third baseman Conor Gillaspie set up Soto, who singled to right. Gillaspie scored, but Soto was thrown out trying to advance to second.

In the bottom of the inning, Twins right fielder Torii Hunter was hit by a pitch and shortstop Eduardo Nunez reached on an infield single. A double down the left-field line by catcher Kurt Suzuki drove in Hunter, but Nunez was gunned down at the plate on a cutoff throw by Ramirez.

NOTES: White Sox RHP Matt Albers threw a simulated game on Tuesday and is set to begin a rehabilitation assignment with Triple-A Charlotte on Friday. Albers has been on the 15-day disabled list on April 25 and had surgery on his fractured pinkie finger on May 5. ... Twins OF Aaron Hicks took batting practice without issue before the game on Tuesday. Hicks has been on the 15-day disabled list since June 14 with a sore right elbow/forearm. ... The White Sox and Twins will finish their three-game series with a contest Wednesday afternoon at Target Field. Chicago will send LHP Chris Sale to the bump (6-3, 2.74 ERA) against Minnesota RHP Phil Hughes (5-6, 4.47 ERA).