ARLINGTON -- Kevin Millwood stood at his locker and spoke about the importance of the Rangers finishing the season strong after leading his team to a sweep over the White Sox.

Millwood knows how beneficial building a winning atmosphere is, even in the midst of a losing season. And he showed he's not giving up after seven strong innings, allowing just one run on six hits, to carry the Rangers past the White Sox, 5-1, for a season-high fifth straight win at Rangers Ballpark in Arlington. It was the Rangers' third sweep of the season, their first against the Sox since Aug. 15-17, 2003.

"We still need to play hard," Millwood said. "I think it's huge for young guys to win some games and know what it takes to win games and win some series. I think everyone here knows what it feels like to lose, so I think it's good for them to know what it takes to win."

After beginning the season 23-42, the Rangers have made quite a turnaround, posting a 38-30 record the last 68 games.

"We stayed the course and didn't give up on those kids," manager Ron Washington said. "They never veered off the course. I see this group has figured out that they can."

And it helps if Millwood continues to pitch like he did on Thursday. It was Millwood's fourth consecutive start that he has gone seven or more innings, a feat he hasn't accomplished since 2003. Millwood credits a move on the pitching rubber, from the third-base side to the first-base side, for his recent success.

"I'm getting more comfortable with it every time out," Millwood said. "Hopefully, I can take some good momentum into next season."

Millwood's performance upended Chicago starter John Danks, whom the Rangers drafted ninth overall in the 2003 First-Year Player Draft. Danks was solid, giving up two earned runs over 5 2/3 innings. But the White Sox defense had four throwing errors, including three by third baseman Andy Gonzalez and the other by Danks, in the third inning, providing the Rangers with three gift runs.

Sammy Sosa capped off the Rangers' victory with a solo home run and an RBI single. Millwood, however, was the most impressive with a 2.12 ERA in his last four starts.

"He's locked in at what he's trying to do and he's executing," Washington said. "He's just being the bulldog we thought he'd be."

Millwood's only hiccup was to White Sox slugger Jim Thome, who continued his march to join the 500-home run club, with a solo shot in the first inning. Thome sent Millwood's 0-1 fastball 422 feet to the right-field seats. That was the only run the White Sox would score. Thome singled and flied out his next two at-bats against Millwood, his former teammate.

"The guy owns me," Millwood said. "He hits me well, what can I say? At least I got the best of him once today."

But Millwood couldn't be more pleased to see Thome closing in on 500 home runs.

"It's awesome," he said. "A guy like that you know there's nothing tainted about him. He's probably one of nicest guys in the league, he was one of the best teammates I've had, so to see him do something special like that is just fun to watch."

Thome had to share a spotlight, though, with another heralded home run hitter in Sosa. Sosa made Danks home run victim No. 368 in the second inning after he belted his 606th career home run just over the center-field fence.

Sosa followed with an RBI single in the fifth. It was an encore performance to Wednesday for Sosa, after he drove in the tying and winning runs.

"I knew I had it, but not like [my last one] against Seattle," Sosa said. "In this ballpark, the ball doesn't jump off the bat, so the wind helped."